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176-640: Spreadsheet users can adjust any stored value and observe the effects on calculated values. This makes the spreadsheet useful for "what-if" analysis since many cases can be rapidly investigated without manual recalculation. Modern spreadsheet software can have multiple interacting sheets and can display data either as text and numerals or in graphical form. Besides performing basic arithmetic and mathematical functions , modern spreadsheets provide built-in functions for common financial accountancy and statistical operations. Such calculations as net present value or standard deviation can be applied to tabular data with

352-432: A data modeling construct for the relational model, and the difference between the two has become irrelevant. The 1980s ushered in the age of desktop computing . The new computers empowered their users with spreadsheets like Lotus 1-2-3 and database software like dBASE . The dBASE product was lightweight and easy for any computer user to understand out of the box. C. Wayne Ratliff , the creator of dBASE, stated: "dBASE

528-666: A database management system. Programs within a suite use similar commands for similar functions. Usually, sharing data between the components is easier than with a non-integrated collection of functionally equivalent programs. This was particularly an advantage at a time when many personal computer systems used text-mode displays and commands instead of a graphical user interface . Humans have organized data into tables , that is, grids of columns and rows, since ancient times. The Babylonians used clay tablets to store data as far back as 1800 BCE. Other examples can be found in book-keeping ledgers and astronomical records. Since at least 1906

704-484: A database management system ( DBMS ), the software that interacts with end users , applications , and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system . Often the term "database" is also used loosely to refer to any of

880-526: A workbook . A workbook is physically represented by a file containing all the data for the book, the sheets, and the cells with the sheets. Worksheets are normally represented by tabs that flip between pages, each one containing one of the sheets, although Numbers changes this model significantly. Cells in a multi-sheet book add the sheet name to their reference, for instance, "Sheet 1!C10". Some systems extend this syntax to allow cell references to different workbooks. Users interact with sheets primarily through

1056-484: A 1962 report by the System Development Corporation of California as the first to use the term "data-base" in a specific technical sense. As computers grew in speed and capability, a number of general-purpose database systems emerged; by the mid-1960s a number of such systems had come into commercial use. Interest in a standard began to grow, and Charles Bachman , author of one such product,

1232-551: A box for holding data . A single cell is usually referenced by its column and row (C2 would represent the cell containing the value 30 in the example table below). Usually rows, representing the dependent variables , are referenced in decimal notation starting from 1, while columns representing the independent variables use 26-adic bijective numeration using the letters A-Z as numerals. Its physical size can usually be tailored to its content by dragging its height or width at box intersections (or for entire columns or rows by dragging

1408-1117: A common denominator. This can be achieved by scaling the first number with the denominator of the second number while scaling the second number with the denominator of the first number. For instance, 1 3 + 1 2 = 1 ⋅ 2 3 ⋅ 2 + 1 ⋅ 3 2 ⋅ 3 = 2 6 + 3 6 = 5 6 {\displaystyle {\tfrac {1}{3}}+{\tfrac {1}{2}}={\tfrac {1\cdot 2}{3\cdot 2}}+{\tfrac {1\cdot 3}{2\cdot 3}}={\tfrac {2}{6}}+{\tfrac {3}{6}}={\tfrac {5}{6}}} . Two rational numbers are multiplied by multiplying their numerators and their denominators respectively, as in 2 3 ⋅ 2 5 = 2 ⋅ 2 3 ⋅ 5 = 4 15 {\displaystyle {\tfrac {2}{3}}\cdot {\tfrac {2}{5}}={\tfrac {2\cdot 2}{3\cdot 5}}={\tfrac {4}{15}}} . Dividing one rational number by another can be achieved by multiplying

1584-440: A custom multitasking kernel with built-in networking support, but modern DBMSs typically rely on a standard operating system to provide these functions. Since DBMSs comprise a significant market , computer and storage vendors often take into account DBMS requirements in their own development plans. Databases and DBMSs can be categorized according to the database model(s) that they support (such as relational or XML ),

1760-443: A database management system. Existing DBMSs provide various functions that allow management of a database and its data which can be classified into four main functional groups: Both a database and its DBMS conform to the principles of a particular database model . "Database system" refers collectively to the database model, database management system, and database. Physically, database servers are dedicated computers that hold

1936-404: A database. One way to classify databases involves the type of their contents, for example: bibliographic , document-text, statistical, or multimedia objects. Another way is by their application area, for example: accounting, music compositions, movies, banking, manufacturing, or insurance. A third way is by some technical aspect, such as the database structure or interface type. This section lists

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2112-543: A different chain, based on IBM's papers on System R. Though Oracle V1 implementations were completed in 1978, it was not until Oracle Version 2 when Ellison beat IBM to market in 1979. Stonebraker went on to apply the lessons from INGRES to develop a new database, Postgres, which is now known as PostgreSQL . PostgreSQL is often used for global mission-critical applications (the .org and .info domain name registries use it as their primary data store , as do many large companies and financial institutions). In Sweden, Codd's paper

2288-463: A different type of entity . Only in the mid-1980s did computing hardware become powerful enough to allow the wide deployment of relational systems (DBMSs plus applications). By the early 1990s, however, relational systems dominated in all large-scale data processing applications, and as of 2018 they remain dominant: IBM Db2 , Oracle , MySQL , and Microsoft SQL Server are the most searched DBMS . The dominant database language, standardized SQL for

2464-423: A few of the adjectives used to characterize different kinds of databases. Connolly and Begg define database management system (DBMS) as a "software system that enables users to define, create, maintain and control access to the database." Examples of DBMS's include MySQL , MariaDB , PostgreSQL , Microsoft SQL Server , Oracle Database , and Microsoft Access . The DBMS acronym is sometimes extended to indicate

2640-442: A general identity element since 1 is not the neutral element for the base. Exponentiation and logarithm are neither commutative nor associative. Different types of arithmetic systems are discussed in the academic literature. They differ from each other based on what type of number they operate on, what numeral system they use to represent them, and whether they operate on mathematical objects other than numbers. Integer arithmetic

2816-410: A limited amount of basic numerals, which directly refer to certain numbers. The system governs how these basic numerals may be combined to express any number. Numeral systems are either positional or non-positional. All early numeral systems were non-positional. For non-positional numeral systems, the value of a digit does not depend on its position in the numeral. The simplest non-positional system

2992-436: A manual request to recalculate since the recalculation of large or complex spreadsheets often reduced data entry speed. Many modern spreadsheets still retain this option. Recalculation generally requires that there are no circular dependencies in a spreadsheet. A dependency graph is a graph that has a vertex for each object to be updated, and an edge connecting two objects whenever one of them needs to be updated earlier than

3168-464: A more complex non-positional numeral system . They have additional symbols for numbers like 10, 100, 1000, and 10,000. These symbols can be combined into a sum to more conveniently express larger numbers. For instance, the numeral for 10,405 uses one time the symbol for 10,000, four times the symbol for 100, and five times the symbol for 1. A similar well-known framework is the Roman numeral system . It has

3344-639: A number, it is also possible to multiply by its reciprocal . The reciprocal of a number is 1 divided by that number. For instance, 48 ÷ 8 = 48 × 1 8 {\displaystyle 48\div 8=48\times {\tfrac {1}{8}}} . The multiplicative identity element is 1 and the multiplicative inverse of a number is the reciprocal of that number. For example, 13 × 1 = 13 {\displaystyle 13\times 1=13} and 13 × 1 13 = 1 {\displaystyle 13\times {\tfrac {1}{13}}=1} . Multiplication

3520-490: A plane. Further branches of number theory are probabilistic number theory , which employs methods from probability theory , combinatorial number theory , which relies on the field of combinatorics , computational number theory , which approaches number-theoretic problems with computational methods, and applied number theory, which examines the application of number theory to fields like physics , biology , and cryptography . Influential theorems in number theory include

3696-553: A positive number as its base. The same is true for the logarithm of positive real numbers as long as the logarithm base is positive and not 1. Irrational numbers involve an infinite non-repeating series of decimal digits. Because of this, there is often no simple and accurate way to express the results of arithmetic operations like 2 + π {\displaystyle {\sqrt {2}}+\pi } or e ⋅ 3 {\displaystyle e\cdot {\sqrt {3}}} . In cases where absolute precision

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3872-473: A pre-programmed function in a formula. Spreadsheet programs also provide conditional expressions, functions to convert between text and numbers, and functions that operate on strings of text. Spreadsheets have replaced paper-based systems throughout the business world. Although they were first developed for accounting or bookkeeping tasks, they now are used extensively in any context where tabular lists are built, sorted, and shared. LANPAR, available in 1969,

4048-507: A range of values if one does not know the precise magnitude, for example, because of measurement errors . Interval arithmetic includes operations like addition and multiplication on intervals, as in [ 1 , 2 ] + [ 3 , 4 ] = [ 4 , 6 ] {\displaystyle [1,2]+[3,4]=[4,6]} and [ 1 , 2 ] × [ 3 , 4 ] = [ 3 , 8 ] {\displaystyle [1,2]\times [3,4]=[3,8]} . It

4224-444: A series of two operations, it does not matter which operation is carried out first. This is the case for multiplication, for example, since ( 5 × 4 ) × 2 {\displaystyle (5\times 4)\times 2} is the same as 5 × ( 4 × 2 ) {\displaystyle 5\times (4\times 2)} . Addition is an arithmetic operation in which two numbers, called

4400-449: A set of operations based on the mathematical system of relational calculus (from which the model takes its name). Splitting the data into a set of normalized tables (or relations ) aimed to ensure that each "fact" was only stored once, thus simplifying update operations. Virtual tables called views could present the data in different ways for different users, but views could not be directly updated. Codd used mathematical terms to define

4576-402: A similar role in the sciences , like physics and economics . Arithmetic is present in many aspects of daily life , for example, to calculate change while shopping or to manage personal finances . It is one of the earliest forms of mathematics education that students encounter. Its cognitive and conceptual foundations are studied by psychology and philosophy . The practice of arithmetic

4752-447: A single large "chunk". Subsequent multi-user versions were tested by customers in 1978 and 1979, by which time a standardized query language – SQL – had been added. Codd's ideas were establishing themselves as both workable and superior to CODASYL, pushing IBM to develop a true production version of System R, known as SQL/DS , and, later, Database 2 ( IBM Db2 ). Larry Ellison 's Oracle Database (or more simply, Oracle ) started from

4928-439: A special type of rational numbers since their denominator is a power of 10. For instance, 0.3 is equal to 3 10 {\displaystyle {\tfrac {3}{10}}} , and 25.12 is equal to 2512 100 {\displaystyle {\tfrac {2512}{100}}} . Every rational number corresponds to a finite or a repeating decimal . Irrational numbers are numbers that cannot be expressed through

5104-452: A strong demand for massively distributed databases with high partition tolerance, but according to the CAP theorem , it is impossible for a distributed system to simultaneously provide consistency , availability, and partition tolerance guarantees. A distributed system can satisfy any two of these guarantees at the same time, but not all three. For that reason, many NoSQL databases are using what

5280-454: A time by navigating the links, they would use a declarative query language that expressed what data was required, rather than the access path by which it should be found. Finding an efficient access path to the data became the responsibility of the database management system, rather than the application programmer. This process, called query optimization, depended on the fact that queries were expressed in terms of mathematical logic. Codd's paper

5456-581: A variant used in VisiCalc and known as "A1 notation". Additionally, spreadsheets have the concept of a range , a group of cells, normally contiguous. For instance, one can refer to the first ten cells in the first column with the range "A1:A10". LANPAR innovated forward referencing/natural order calculation which didn't re-appear until Lotus 123 and Microsoft's MultiPlan Version 2. In modern spreadsheet applications, several spreadsheets, often known as worksheets or simply sheets , are gathered together to form

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5632-416: A version that ran on IBM mainframes was introduced under the name AutoTab . ( National CSS offered a similar product, CSSTAB, which had a moderate timesharing user base by the early 1970s. A major application was opinion research tabulation.) AutoPlan/AutoTab was not a WYSIWYG interactive spreadsheet program, it was a simple scripting language for spreadsheets. The user defined the names and labels for

5808-467: A web-based spreadsheet application XL2Web developed by 2Web Technologies , combined with DocVerse which enabled multiple-user online collaboration of Office documents. In 2016 Collabora Online Calc was launched, notable in that the web based spreadsheet could be hosted and integrated into any environment without dependency on a 3rd party for authentication or maintenance. Collabora Online runs LibreOffice kit at its core, which grew from StarOffice that

5984-556: Is exponentiation by squaring . It breaks down the calculation into a number of squaring operations. For example, the exponentiation 3 65 {\displaystyle 3^{65}} can be written as ( ( ( ( ( 3 2 ) 2 ) 2 ) 2 ) 2 ) 2 × 3 {\displaystyle (((((3^{2})^{2})^{2})^{2})^{2})^{2}\times 3} . By taking advantage of repeated squaring operations, only 7 individual operations are needed rather than

6160-406: Is 0 and the additive inverse of a number is the negative of that number. For instance, 13 + 0 = 13 {\displaystyle 13+0=13} and 13 + ( − 13 ) = 0 {\displaystyle 13+(-13)=0} . Addition is both commutative and associative. Multiplication is an arithmetic operation in which two numbers, called the multiplier and

6336-426: Is 0. 3 . Every repeating decimal expresses a rational number. Real number arithmetic is the branch of arithmetic that deals with the manipulation of both rational and irrational numbers. Irrational numbers are numbers that cannot be expressed through fractions or repeated decimals, like the root of 2 and π . Unlike rational number arithmetic, real number arithmetic is closed under exponentiation as long as it uses

6512-545: Is a prime number that has no other prime factorization. Euclid's theorem states that there are infinitely many prime numbers. Fermat's last theorem is the statement that no positive integer values can be found for a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} , to solve the equation a n + b n = c n {\displaystyle a^{n}+b^{n}=c^{n}} if n {\displaystyle n}

6688-465: Is a relatively crude method, with some unintuitive subtleties; explicitly keeping track of an estimate or upper bound of the approximation error is a more sophisticated approach. In the example, the person's height might be represented as 1.62 ± 0.005 meters or 63.8 ± 0.2 inches . In performing calculations with uncertain quantities, the uncertainty should be propagated to calculated quantities. When adding or subtracting two or more quantities, add

6864-902: Is a similar process in which the last preserved digit is increased by one if the next digit is 5 or greater but remains the same if the next digit is less than 5, so that the rounded number is the best approximation of a given precision for the original number. For instance, if the number π is rounded to 4 decimal places, the result is 3.142 because the following digit is a 5, so 3.142 is closer to π than 3.141. These methods allow computers to efficiently perform approximate calculations on real numbers. In science and engineering, numbers represent estimates of physical quantities derived from measurement or modeling. Unlike mathematically exact numbers such as π or ⁠ 2 {\displaystyle {\sqrt {2}}} ⁠ , scientifically relevant numerical data are inherently inexact, involving some measurement uncertainty . One basic way to express

7040-414: Is about calculations with real numbers , which include both rational and irrational numbers . Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers . Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of

7216-507: Is an elementary branch of mathematics that studies numerical operations like addition , subtraction , multiplication , and division . In a wider sense, it also includes exponentiation , extraction of roots , and taking logarithms . Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers . Rational number arithmetic involves operations on fractions of integers. Real number arithmetic

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7392-450: Is an inverse of the operation " ∘ {\displaystyle \circ } " if it fulfills the following condition: t ⋆ s = r {\displaystyle t\star s=r} if and only if r ∘ s = t {\displaystyle r\circ s=t} . Commutativity and associativity are laws governing the order in which some arithmetic operations can be carried out. An operation

7568-436: Is applied to another element. For example, the identity element of addition is 0 since any sum of a number and 0 results in the same number. The inverse element is the element that results in the identity element when combined with another element. For instance, the additive inverse of the number 6 is -6 since their sum is 0. There are not only inverse elements but also inverse operations . In an informal sense, one operation

7744-526: Is at least thousands and possibly tens of thousands of years old. Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE. Starting in the 7th and 6th centuries BCE, the ancient Greeks initiated a more abstract study of numbers and introduced the method of rigorous mathematical proofs . The ancient Indians developed

7920-583: Is both commutative and associative. Exponentiation is an arithmetic operation in which a number, known as the base, is raised to the power of another number, known as the exponent. The result of this operation is called the power. Exponentiation is sometimes expressed using the symbol ^ but the more common way is to write the exponent in superscript right after the base. Examples are 2 4 = 16 {\displaystyle 2^{4}=16} and 3 {\displaystyle 3} ^ 3 = 27 {\displaystyle 3=27} . If

8096-960: Is called eventual consistency to provide both availability and partition tolerance guarantees with a reduced level of data consistency. NewSQL is a class of modern relational databases that aims to provide the same scalable performance of NoSQL systems for online transaction processing (read-write) workloads while still using SQL and maintaining the ACID guarantees of a traditional database system. Databases are used to support internal operations of organizations and to underpin online interactions with customers and suppliers (see Enterprise software ). Databases are used to hold administrative information and more specialized data, such as engineering data or economic models. Examples include computerized library systems, flight reservation systems , computerized parts inventory systems , and many content management systems that store websites as collections of webpages in

8272-515: Is classified by IBM as a hierarchical database . IDMS and Cincom Systems ' TOTAL databases are classified as network databases. IMS remains in use as of 2014 . Edgar F. Codd worked at IBM in San Jose, California , in one of their offshoot offices that were primarily involved in the development of hard disk systems. He was unhappy with the navigational model of the CODASYL approach, notably

8448-403: Is closed under division as long as the divisor is not 0. Both integer arithmetic and rational number arithmetic are not closed under exponentiation and logarithm. One way to calculate exponentiation with a fractional exponent is to perform two separate calculations: one exponentiation using the numerator of the exponent followed by drawing the nth root of the result based on the denominator of

8624-400: Is closely related to affine arithmetic, which aims to give more precise results by performing calculations on affine forms rather than intervals. An affine form is a number together with error terms that describe how the number may deviate from the actual magnitude. Database In computing , a database is an organized collection of data or a type of data store based on the use of

8800-401: Is commutative if the order of the arguments can be changed without affecting the results. This is the case for addition, for instance, 7 + 9 {\displaystyle 7+9} is the same as 9 + 7 {\displaystyle 9+7} . Associativity is a rule that affects the order in which a series of operations can be carried out. An operation is associative if, in

8976-431: Is greater than 2 {\displaystyle 2} . Rational number arithmetic is the branch of arithmetic that deals with the manipulation of numbers that can be expressed as a ratio of two integers. Most arithmetic operations on rational numbers can be calculated by performing a series of integer arithmetic operations on the numerators and the denominators of the involved numbers. If two rational numbers have

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9152-463: Is indistinguishable from a batch compiler with added input data, producing an output report, i.e. , a 4GL or conventional, non-interactive, batch computer program. However, this concept of an electronic spreadsheet was outlined in the 1961 paper "Budgeting Models and System Simulation" by Richard Mattessich . The subsequent work by Mattessich (1964a, Chpt. 9, Accounting and Analytical Methods ) and its companion volume, Mattessich (1964b, Simulation of

9328-439: Is infinite without repeating decimals. The set of rational numbers together with the set of irrational numbers makes up the set of real numbers. The symbol of the real numbers is R {\displaystyle \mathbb {R} } . Even wider classes of numbers include complex numbers and quaternions . A numeral is a symbol to represent a number and numeral systems are representational frameworks. They usually have

9504-427: Is not closed under division. This means that when dividing one integer by another integer, the result is not always an integer. For instance, 7 divided by 2 is not a whole number but 3.5. One way to ensure that the result is an integer is to round the result to a whole number. However, this method leads to inaccuracies as the original value is altered. Another method is to perform the division only partially and retain

9680-417: Is not required, the problem of calculating arithmetic operations on real numbers is usually addressed by truncation or rounding . For truncation, a certain number of leftmost digits are kept and remaining digits are discarded or replaced by zeros. For example, the number π has an infinite number of digits starting with 3.14159.... If this number is truncated to 4 decimal places, the result is 3.141. Rounding

9856-437: Is often treated as a special case of addition: instead of subtracting a positive number, it is also possible to add a negative number. For instance 14 − 8 = 14 + ( − 8 ) {\displaystyle 14-8=14+(-8)} . This helps to simplify mathematical computations by reducing the number of basic arithmetic operations needed to perform calculations. The additive identity element

10032-411: Is organized. Because of the close relationship between them, the term "database" is often used casually to refer to both a database and the DBMS used to manipulate it. Outside the world of professional information technology , the term database is often used to refer to any collection of related data (such as a spreadsheet or a card index) as size and usage requirements typically necessitate use of

10208-930: Is restricted to the study of integers and focuses on their properties and relationships such as divisibility , factorization , and primality . Traditionally, it is known as higher arithmetic. Numbers are mathematical objects used to count quantities and measure magnitudes. They are fundamental elements in arithmetic since all arithmetic operations are performed on numbers. There are different kinds of numbers and different numeral systems to represent them. The main kinds of numbers employed in arithmetic are natural numbers , whole numbers, integers , rational numbers , and real numbers . The natural numbers are whole numbers that start from 1 and go to infinity. They exclude 0 and negative numbers. They are also known as counting numbers and can be expressed as { 1 , 2 , 3 , 4 , . . . } {\displaystyle \{1,2,3,4,...\}} . The symbol of

10384-421: Is still pursued in certain applications by some companies like Netezza and Oracle ( Exadata ). IBM started working on a prototype system loosely based on Codd's concepts as System R in the early 1970s. The first version was ready in 1974/5, and work then started on multi-table systems in which the data could be split so that all of the data for a record (some of which is optional) did not have to be stored in

10560-517: Is the unary numeral system . It relies on one symbol for the number 1. All higher numbers are written by repeating this symbol. For example, the number 7 can be represented by repeating the symbol for 1 seven times. This system makes it cumbersome to write large numbers, which is why many non-positional systems include additional symbols to directly represent larger numbers. Variations of the unary numeral systems are employed in tally sticks using dents and in tally marks . Egyptian hieroglyphics had

10736-404: Is the basis of query optimization. There is no loss of expressiveness compared with the hierarchic or network models, though the connections between tables are no longer so explicit. In the hierarchic and network models, records were allowed to have a complex internal structure. For example, the salary history of an employee might be represented as a "repeating group" within the employee record. In

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10912-462: Is the branch of arithmetic that deals with the manipulation of positive and negative whole numbers. Simple one-digit operations can be performed by following or memorizing a table that presents the results of all possible combinations, like an addition table or a multiplication table . Other common methods are verbal counting and finger-counting . For operations on numbers with more than one digit, different techniques can be employed to calculate

11088-428: Is the inverse of another operation if it undoes the first operation. For example, subtraction is the inverse of addition since a number returns to its original value if a second number is first added and subsequently subtracted, as in 13 + 4 − 4 = 13 {\displaystyle 13+4-4=13} . Defined more formally, the operation " ⋆ {\displaystyle \star } "

11264-413: Is the inverse of exponentiation. The logarithm of a number x {\displaystyle x} to the base b {\displaystyle b} is the exponent to which b {\displaystyle b} must be raised to produce x {\displaystyle x} . For instance, since 1000 = 10 3 {\displaystyle 1000=10^{3}} ,

11440-591: The Hindu–Arabic numeral system , the radix is 10. This means that the first digit is multiplied by 10 0 {\displaystyle 10^{0}} , the next digit is multiplied by 10 1 {\displaystyle 10^{1}} , and so on. For example, the decimal numeral 532 stands for 5 ⋅ 10 2 + 3 ⋅ 10 1 + 2 ⋅ 10 0 {\displaystyle 5\cdot 10^{2}+3\cdot 10^{1}+2\cdot 10^{0}} . Because of

11616-667: The Integrated Data Store (IDS), founded the Database Task Group within CODASYL , the group responsible for the creation and standardization of COBOL . In 1971, the Database Task Group delivered their standard, which generally became known as the CODASYL approach , and soon a number of commercial products based on this approach entered the market. The CODASYL approach offered applications

11792-599: The Michigan Terminal System . The system remained in production until 1998. In the 1970s and 1980s, attempts were made to build database systems with integrated hardware and software. The underlying philosophy was that such integration would provide higher performance at a lower cost. Examples were IBM System/38 , the early offering of Teradata , and the Britton Lee, Inc. database machine. Another approach to hardware support for database management

11968-428: The absolute uncertainties of each summand together to obtain the absolute uncertainty of the sum. When multiplying or dividing two or more quantities, add the relative uncertainties of each factor together to obtain the relative uncertainty of the product. When representing uncertainty by significant digits, uncertainty can be coarsely propagated by rounding the result of adding or subtracting two or more quantities to

12144-434: The database models that they support. Relational databases became dominant in the 1980s. These model data as rows and columns in a series of tables , and the vast majority use SQL for writing and querying data. In the 2000s, non-relational databases became popular, collectively referred to as NoSQL , because they use different query languages . Formally, a "database" refers to a set of related data accessed through

12320-494: The fundamental theorem of arithmetic , Euclid's theorem , and Fermat's last theorem . According to the fundamental theorem of arithmetic, every integer greater than 1 is either a prime number or can be represented as a unique product of prime numbers. For example, the number 18 is not a prime number and can be represented as 2 × 3 × 3 {\displaystyle 2\times 3\times 3} , all of which are prime numbers. The number 19 , by contrast,

12496-471: The hierarchical model and the CODASYL model ( network model ). These were characterized by the use of pointers (often physical disk addresses) to follow relationships from one record to another. The relational model , first proposed in 1970 by Edgar F. Codd , departed from this tradition by insisting that applications should search for data by content, rather than by following links. The relational model employs sets of ledger-style tables, each used for

12672-589: The lattice method . Computer science is interested in multiplication algorithms with a low computational complexity to be able to efficiently multiply very large integers, such as the Karatsuba algorithm , the Schönhage–Strassen algorithm , and the Toom–Cook algorithm . A common technique used for division is called long division . Other methods include short division and chunking . Integer arithmetic

12848-426: The personal computer from a hobby for computer enthusiasts into a business tool. VisiCalc was the first spreadsheet that combined many of the essential features of modern spreadsheet applications, such as a WYSIWYG interactive user interface, automatic recalculation, status and formula lines, range copying with relative and absolute references, and formula building by selecting referenced cells. Unaware of LANPAR at

13024-461: The professor and manipulate it to represent it and show ratios etc. In 1964, a book entitled Business Computer Language was written by Kimball, Stoffells and Walsh. Both the book and program were copyrighted in 1966 and years later that copyright was renewed. Applied Data Resources had a FORTRAN preprocessor called Empires. In the late 1960s, Xerox used BCL to develop a more sophisticated version for their timesharing system. A key invention in

13200-431: The quotient . The symbols of division are ÷ {\displaystyle \div } and / {\displaystyle /} . Examples are 48 ÷ 8 = 6 {\displaystyle 48\div 8=6} and 29.4 / 1.4 = 21 {\displaystyle 29.4/1.4=21} . Division is often treated as a special case of multiplication: instead of dividing by

13376-400: The relational structure of a database. Spreadsheets and databases are interoperable—sheets can be imported into databases to become tables within them, and database queries can be exported into spreadsheets for further analysis. A spreadsheet program is one of the main components of an office productivity suite , which usually also contains a word processor , a presentation program , and

13552-568: The remainder . For example, 7 divided by 2 is 3 with a remainder of 1. These difficulties are avoided by rational number arithmetic, which allows for the exact representation of fractions. A simple method to calculate exponentiation is by repeated multiplication. For instance, the exponentiation of 3 4 {\displaystyle 3^{4}} can be calculated as 3 × 3 × 3 × 3 {\displaystyle 3\times 3\times 3\times 3} . A more efficient technique used for large exponents

13728-622: The 1980s and early 1990s. The 1990s, along with a rise in object-oriented programming , saw a growth in how data in various databases were handled. Programmers and designers began to treat the data in their databases as objects . That is to say that if a person's data were in a database, that person's attributes, such as their address, phone number, and age, were now considered to belong to that person instead of being extraneous data. This allows for relations between data to be related to objects and their attributes and not to individual fields. The term " object–relational impedance mismatch " described

13904-452: The 64 operations required for regular repeated multiplication. Methods to calculate logarithms include the Taylor series and continued fractions . Integer arithmetic is not closed under logarithm and under exponentiation with negative exponents, meaning that the result of these operations is not always an integer. Number theory studies the structure and properties of integers as well as

14080-740: The Apple II, this helped it grow in popularity. Lotus 1-2-3 was the leading spreadsheet for several years. Microsoft released the first version of Excel for the Apple Macintosh on September 30, 1985, and then ported it to Windows, with the first version being numbered 2.05 (to synchronize with the Macintosh version 2.2) and released in November 1987. Microsoft's Windows 3.x platforms of the early 1990s made it possible for their Excel spreadsheet application to take market share from Lotus. By

14256-596: The DBMS, the database system or an application associated with the database. Small databases can be stored on a file system , while large databases are hosted on computer clusters or cloud storage . The design of databases spans formal techniques and practical considerations, including data modeling , efficient data representation and storage, query languages , security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance . Computer scientists may classify database management systems according to

14432-584: The Federal Circuit (CCPA), overturning the Patent Office in 1983 — establishing that "something does not cease to become patentable merely because the point of novelty is in an algorithm." However, in 1995 a federal district court ruled the patent unenforceable due to inequitable conduct by the inventors during the application process. The United States Court of Appeals for the Federal Circuit upheld that decision in 1996. The actual software

14608-519: The Firm through a Budget Computer Program ) applied computerized spreadsheets to accounting and budgeting systems (on mainframe computers programmed in FORTRAN IV ). These batch Spreadsheets dealt primarily with the addition or subtraction of entire columns or rows (of input variables), rather than individual cells . In 1962, this concept of the spreadsheet, called BCL for Business Computer Language,

14784-658: The Latin term " arithmetica " which derives from the Ancient Greek words ἀριθμός (arithmos), meaning "number", and ἀριθμητική τέχνη (arithmetike tekhne), meaning "the art of counting". There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers . However, the more common view is to include operations on integers , rational numbers , real numbers , and sometimes also complex numbers in its scope. Some definitions restrict arithmetic to

14960-686: The University of Michigan began development of the MICRO Information Management System based on D.L. Childs ' Set-Theoretic Data model. MICRO was used to manage very large data sets by the US Department of Labor , the U.S. Environmental Protection Agency , and researchers from the University of Alberta , the University of Michigan , and Wayne State University . It ran on IBM mainframe computers using

15136-461: The X and Y locations. X locations, the columns, are normally represented by letters, "A," "B," "C," etc., while rows are normally represented by numbers, 1, 2, 3, etc. A single cell can be referred to by addressing its row and column, "C10". This electronic concept of cell references was first introduced in LANPAR (Language for Programming Arrays at Random) (co-invented by Rene Pardo and Remy Landau) and

15312-539: The ability to navigate around a linked data set which was formed into a large network. Applications could find records by one of three methods: Later systems added B-trees to provide alternate access paths. Many CODASYL databases also added a declarative query language for end users (as distinct from the navigational API ). However, CODASYL databases were complex and required significant training and effort to produce useful applications. IBM also had its own DBMS in 1966, known as Information Management System (IMS). IMS

15488-457: The accuracy and speed with which arithmetic calculations could be performed. Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition , subtraction , multiplication , and division . In a wider sense, it also includes exponentiation , extraction of roots , and logarithm . The term "arithmetic" has its root in

15664-438: The actual databases and run only the DBMS and related software. Database servers are usually multiprocessor computers, with generous memory and RAID disk arrays used for stable storage. Hardware database accelerators, connected to one or more servers via a high-speed channel, are also used in large-volume transaction processing environments . DBMSs are found at the heart of most database applications . DBMSs may be built around

15840-435: The addends, are combined into a single number, called the sum. The symbol of addition is + {\displaystyle +} . Examples are 2 + 2 = 4 {\displaystyle 2+2=4} and 6.3 + 1.26 = 7.56 {\displaystyle 6.3+1.26=7.56} . The term summation is used if several additions are performed in a row. Counting is a type of repeated addition in which

16016-510: The base can be understood from context. So, the previous example can be written log 10 ⁡ 1000 = 3 {\displaystyle \log _{10}1000=3} . Exponentiation and logarithm do not have general identity elements and inverse elements like addition and multiplication. The neutral element of exponentiation in relation to the exponent is 1, as in 14 1 = 14 {\displaystyle 14^{1}=14} . However, exponentiation does not have

16192-401: The basic numerals 0 and 1. Computer arithmetic deals with the specificities of the implementation of binary arithmetic on computers . Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic. Arithmetic operations form the basis of many branches of mathematics, such as algebra , calculus , and statistics . They play

16368-438: The business plans that they were presenting to venture capitalists. They decided to save themselves a lot of effort and wrote a computer program that produced their tables for them. This program, originally conceived as a simple utility for their personal use, would turn out to be the first software product offered by the company that would become known as Capex Corporation . "AutoPlan" ran on GE's Time-sharing service; afterward,

16544-416: The cell itself. Alternatively, a value can be based on a formula (see below), which might perform a calculation, display the current date or time, or retrieve external data such as a stock quote or a database value. The Spreadsheet Value Rule Computer scientist Alan Kay used the term value rule to summarize a spreadsheet's operation: a cell's value relies solely on the formula the user has typed into

16720-403: The cell. The formula may rely on the value of other cells, but those cells are likewise restricted to user-entered data or formulas. There are no 'side effects' to calculating a formula: the only output is to display the calculated result inside its occupying cell. There is no natural mechanism for permanently modifying the contents of a cell unless the user manually modifies the cell's contents. In

16896-420: The cells. A given cell can hold data by simply entering it in, or a formula, which is normally created by preceding the text with an equals sign. Data might include the string of text hello world , the number 5 or the date 10-Sep-97 . A formula would begin with the equals sign, =5*3 , but this would normally be invisible because the display shows the result of the calculation, 15 in this case, not

17072-440: The claim that every even number is a sum of two prime numbers . Algebraic number theory employs algebraic structures to analyze the properties of and relations between numbers. Examples are the use of fields and rings , as in algebraic number fields like the ring of integers . Geometric number theory uses concepts from geometry to study numbers. For instance, it investigates how lattice points with integer coordinates behave in

17248-418: The column- or row-headers). An array of cells is called a sheet or worksheet . It is analogous to an array of variables in a conventional computer program (although certain unchanging values, once entered, could be considered, by the same analogy, constants ). In most implementations, many worksheets may be located within a single spreadsheet. A worksheet is simply a subset of the spreadsheet divided for

17424-502: The concept of zero and the decimal system , which Arab mathematicians further refined and spread to the Western world during the medieval period. The first mechanical calculators were invented in the 17th century. The 18th and 19th centuries saw the development of modern number theory and the formulation of axiomatic foundations of arithmetic. In the 20th century, the emergence of electronic calculators and computers revolutionized

17600-425: The context of programming languages, this yields a limited form of first-order functional programming . A standard of spreadsheets since the 1980s, this optional feature eliminates the need to manually request the spreadsheet program to recalculate values (nowadays typically the default option unless specifically 'switched off' for large spreadsheets, usually to improve performance). Some earlier spreadsheets required

17776-488: The decimal fraction notation. Modified versions of integer calculation methods like addition with carry and long multiplication can be applied to calculations with decimal fractions. Not all rational numbers have a finite representation in the decimal notation. For example, the rational number 1 3 {\displaystyle {\tfrac {1}{3}}} corresponds to 0.333... with an infinite number of 3s. The shortened notation for this type of repeating decimal

17952-522: The degree of certainty about each number's value and avoid false precision is to round each measurement to a certain number of digits, called significant digits , which are implied to be accurate. For example, a person's height measured with a tape measure might only be precisely known to the nearest centimeter, so should be presented as 1.62 meters rather than 1.6217 meters. If converted to imperial units, this quantity should be rounded to 64 inches or 63.8 inches rather than 63.7795 inches, to clearly convey

18128-576: The desired level of accuracy. The Taylor series or the continued fraction method can be utilized to calculate logarithms. The decimal fraction notation is a special way of representing rational numbers whose denominator is a power of 10. For instance, the rational numbers 1 10 {\displaystyle {\tfrac {1}{10}}} , 371 100 {\displaystyle {\tfrac {371}{100}}} , and 44 10000 {\displaystyle {\tfrac {44}{10000}}} are written as 0.1, 3.71, and 0.0044 in

18304-470: The development of electronic spreadsheets was made by Rene K. Pardo and Remy Landau, who filed in 1970 U.S. patent 4,398,249 on a spreadsheet automatic natural order calculation algorithm . While the patent was initially rejected by the patent office as being a purely mathematical invention, following 12 years of appeals, Pardo and Landau won a landmark court case at the Predecessor Court of

18480-652: The distinction between the natural and the whole numbers by including 0 in the set of natural numbers. The set of integers encompasses both positive and negative whole numbers. It has the symbol Z {\displaystyle \mathbb {Z} } and can be expressed as { . . . , − 2 , − 1 , 0 , 1 , 2 , . . . } {\displaystyle \{...,-2,-1,0,1,2,...\}} . Based on how natural and whole numbers are used, they can be distinguished into cardinal and ordinal numbers . Cardinal numbers, like one, two, and three, are numbers that express

18656-475: The effect of the digits' positions, the numeral 532 differs from the numerals 325 and 253 even though they have the same digits. Another positional numeral system used extensively in computer arithmetic is the binary system , which has a radix of 2. This means that the first digit is multiplied by 2 0 {\displaystyle 2^{0}} , the next digit by 2 1 {\displaystyle 2^{1}} , and so on. For example,

18832-455: The entire spreadsheet) can optionally be "locked" to prevent accidental overwriting. Typically this would apply to cells containing formulas but might apply to cells containing "constants" such as a kilogram/pounds conversion factor (2.20462262 to eight decimal places). Even though individual cells are marked as locked, the spreadsheet data are not protected until the feature is activated in the file preferences. Arithmetic Arithmetic

19008-408: The exponent is a natural number then exponentiation is the same as repeated multiplication, as in 2 4 = 2 × 2 × 2 × 2 {\displaystyle 2^{4}=2\times 2\times 2\times 2} . Roots are a special type of exponentiation using a fractional exponent. For example, the square root of a number is the same as raising the number to

19184-458: The exponent. For example, 5 2 3 = 5 2 3 {\displaystyle 5^{\frac {2}{3}}={\sqrt[{3}]{5^{2}}}} . The first operation can be completed using methods like repeated multiplication or exponentiation by squaring. One way to get an approximate result for the second operation is to employ Newton's method , which uses a series of steps to gradually refine an initial guess until it reaches

19360-421: The field of numerical calculations. When understood in a wider sense, it also includes the study of how the concept of numbers developed, the analysis of properties of and relations between numbers, and the examination of the axiomatic structure of arithmetic operations. Arithmetic is closely related to number theory and some authors use the terms as synonyms. However, in a more specific sense, number theory

19536-403: The first "non-procedural" computer languages) as opposed to left-to-right, top to bottom sequence for calculating the results in each cell that was used by VisiCalc , SuperCalc , and the first version of MultiPlan . Without forward referencing/natural order calculation, the user had to refresh the spreadsheet until the values in all cells remained unchanged. Once the cell values stayed constant,

19712-483: The first number with the reciprocal of the second number. This means that the numerator and the denominator of the second number change position. For example, 3 5 : 2 7 = 3 5 ⋅ 7 2 = 21 10 {\displaystyle {\tfrac {3}{5}}:{\tfrac {2}{7}}={\tfrac {3}{5}}\cdot {\tfrac {7}{2}}={\tfrac {21}{10}}} . Unlike integer arithmetic, rational number arithmetic

19888-411: The formula itself. This may lead to confusion in some cases. The key feature of spreadsheets is the ability for a formula to refer to the contents of other cells, which may, in turn, be the result of a formula. To make such a formula, one replaces a number with a cell reference. For instance, the formula =5*C10 would produce the result of multiplying the value in cell C10 by the number 5. If C10 holds

20064-400: The inconvenience of translating between programmed objects and database tables. Object databases and object–relational databases attempt to solve this problem by providing an object-oriented language (sometimes as extensions to SQL) that programmers can use as alternative to purely relational SQL. On the programming side, libraries known as object–relational mappings (ORMs) attempt to solve

20240-502: The integer 1, called the numerator, by the integer 2, called the denominator. Other examples are 3 4 {\displaystyle {\tfrac {3}{4}}} and 281 3 {\displaystyle {\tfrac {281}{3}}} . The set of rational numbers includes all integers, which are fractions with a denominator of 1. The symbol of the rational numbers is Q {\displaystyle \mathbb {Q} } . Decimal fractions like 0.3 and 25.12 are

20416-430: The lack of a "search" facility. In 1970, he wrote a number of papers that outlined a new approach to database construction that eventually culminated in the groundbreaking A Relational Model of Data for Large Shared Data Banks . In this paper, he described a new system for storing and working with large databases. Instead of records being stored in some sort of linked list of free-form records as in CODASYL, Codd's idea

20592-528: The largest market share on the Windows and Macintosh platforms. A spreadsheet program is a standard feature of an office productivity suite . In 2006 Google launched a beta release spreadsheet web application , this is currently known as Google Sheets and one of the applications provided in Google Drive . A spreadsheet consists of a table of cells arranged into rows and columns and referred to by

20768-493: The left. This process is repeated until all digits have been added. Other methods used for integer additions are the number line method, the partial sum method, and the compensation method. A similar technique is utilized for subtraction: it also starts with the rightmost digit and uses a "borrow" or a negative carry for the column on the left if the result of the one-digit subtraction is negative. A basic technique of integer multiplication employs repeated addition. For example,

20944-458: The leftmost last significant decimal place among the summands, and by rounding the result of multiplying or dividing two or more quantities to the least number of significant digits among the factors. (See Significant figures § Arithmetic .) More sophisticated methods of dealing with uncertain values include interval arithmetic and affine arithmetic . Interval arithmetic describes operations on intervals . Intervals can be used to represent

21120-610: The legacy batch system into each user's spreadsheet monthly. It was designed to optimize the power of APL through object kernels, increasing program efficiency by as much as 50 fold over traditional programming approaches. An example of an early "industrial weight" spreadsheet was APLDOT, developed in 1976 at the United States Railway Association on an IBM 360/91, running at The Johns Hopkins University Applied Physics Laboratory in Laurel, MD. The application

21296-492: The logarithm base 10 of 1000 is 3. The logarithm of x {\displaystyle x} to base b {\displaystyle b} is denoted as log b ⁡ ( x ) {\displaystyle \log _{b}(x)} , or without parentheses, log b ⁡ x {\displaystyle \log _{b}x} , or even without the explicit base, log ⁡ x {\displaystyle \log x} , when

21472-534: The model to view results of underlying formulas. His idea became VisiCalc. VisiCalc for the Apple II went on to become the first killer application , a program so compelling, people would buy a particular computer just to use it. It was ported to other computers, including CP/M machines, Atari 8-bit computers , and the Commodore PET , but VisiCalc remains best known as an Apple II program. SuperCalc

21648-576: The model: relations, tuples, and domains rather than tables, rows, and columns. The terminology that is now familiar came from early implementations. Codd would later criticize the tendency for practical implementations to depart from the mathematical foundations on which the model was based. The use of primary keys (user-oriented identifiers) to represent cross-table relationships, rather than disk addresses, had two primary motivations. From an engineering perspective, it enabled tables to be relocated and resized without expensive database reorganization. But Codd

21824-407: The multiplicand is a natural number then multiplication is the same as repeated addition, as in 2 × 3 = 2 + 2 + 2 {\displaystyle 2\times 3=2+2+2} . Division is the inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor. The result of this operation is called

22000-433: The multiplicand, are combined into a single number called the product . The symbols of multiplication are × {\displaystyle \times } , ⋅ {\displaystyle \cdot } , and *. Examples are 2 × 3 = 6 {\displaystyle 2\times 3=6} and 0.3 ⋅ 5 = 1.5 {\displaystyle 0.3\cdot 5=1.5} . If

22176-484: The natural numbers is N {\displaystyle \mathbb {N} } . The whole numbers are identical to the natural numbers with the only difference being that they include 0. They can be represented as { 0 , 1 , 2 , 3 , 4 , . . . } {\displaystyle \{0,1,2,3,4,...\}} and have the symbol N 0 {\displaystyle \mathbb {N} _{0}} . Some mathematicians do not draw

22352-512: The number 1 is continuously added. Subtraction is the inverse of addition. In it, one number, known as the subtrahend, is taken away from another, known as the minuend. The result of this operation is called the difference. The symbol of subtraction is − {\displaystyle -} . Examples are 14 − 8 = 6 {\displaystyle 14-8=6} and 45 − 1.7 = 43.3 {\displaystyle 45-1.7=43.3} . Subtraction

22528-430: The number 13 is written as 1101 in the binary notation, which stands for 1 ⋅ 2 3 + 1 ⋅ 2 2 + 0 ⋅ 2 1 + 1 ⋅ 2 0 {\displaystyle 1\cdot 2^{3}+1\cdot 2^{2}+0\cdot 2^{1}+1\cdot 2^{0}} . In computing, each digit in the binary notation corresponds to one bit . The earliest positional system

22704-438: The numbers within a range. Spreadsheets share many principles and traits of databases , but spreadsheets and databases are not the same things. A spreadsheet is essentially just one table, whereas a database is a collection of many tables with machine-readable semantic relationships. While it is true that a workbook that contains three sheets is indeed a file containing multiple tables that can interact with each other, it lacks

22880-541: The other. Dependency graphs without circular dependencies form directed acyclic graphs , representations of partial orderings (in this case, across a spreadsheet) that can be relied upon to give a definite result. This feature refers to updating a cell's contents periodically with a value from an external source—such as a cell in a "remote" spreadsheet. For shared, Web-based spreadsheets, it applies to "immediately" updating cells another user has updated. All dependent cells must be updated also. Once entered, selected cells (or

23056-547: The power of 1 2 {\displaystyle {\tfrac {1}{2}}} and the cube root of a number is the same as raising the number to the power of 1 3 {\displaystyle {\tfrac {1}{3}}} . Examples are 4 = 4 1 2 = 2 {\displaystyle {\sqrt {4}}=4^{\frac {1}{2}}=2} and 27 3 = 27 1 3 = 3 {\displaystyle {\sqrt[{3}]{27}}=27^{\frac {1}{3}}=3} . Logarithm

23232-418: The precision of the measurement. When a number is written using ordinary decimal notation, leading zeros are not significant, and trailing zeros of numbers not written with a decimal point are implicitly considered to be non-significant. For example, the numbers 0.056 and 1200 each have only 2 significant digits, but the number 40.00 has 4 significant digits. Representing uncertainty using only significant digits

23408-414: The product of 3 × 4 {\displaystyle 3\times 4} can be calculated as 3 + 3 + 3 + 3 {\displaystyle 3+3+3+3} . A common technique for multiplication with larger numbers is called long multiplication . This method starts by writing the multiplier above the multiplicand. The calculation begins by multiplying the multiplier only with

23584-418: The programming language from the end-user. Through IBM's VM operating system , it was among the first programs to auto-update each copy of the application as new versions were released. Users could specify simple mathematical relationships between rows and between columns. Compared to any contemporary alternatives, it could support very large spreadsheets. It loaded actual financial planning data drawn from

23760-411: The quantity of objects. They answer the question "how many?". Ordinal numbers, such as first, second, and third, indicate order or placement in a series. They answer the question "what position?". A number is rational if it can be represented as the ratio of two integers. For instance, the rational number 1 2 {\displaystyle {\tfrac {1}{2}}} is formed by dividing

23936-441: The ratio of two integers. They are often required to describe geometric magnitudes. For example, if a right triangle has legs of the length 1 then the length of its hypotenuse is given by the irrational number 2 {\displaystyle {\sqrt {2}}} . π is another irrational number and describes the ratio of a circle 's circumference to its diameter . The decimal representation of an irrational number

24112-480: The relational approach, the data would be normalized into a user table, an address table and a phone number table (for instance). Records would be created in these optional tables only if the address or phone numbers were actually provided. As well as identifying rows/records using logical identifiers rather than disk addresses, Codd changed the way in which applications assembled data from multiple records. Rather than requiring applications to gather data one record at

24288-599: The relational model, has influenced database languages for other data models. Object databases were developed in the 1980s to overcome the inconvenience of object–relational impedance mismatch , which led to the coining of the term "post-relational" and also the development of hybrid object–relational databases . The next generation of post-relational databases in the late 2000s became known as NoSQL databases, introducing fast key–value stores and document-oriented databases . A competing "next generation" known as NewSQL databases attempted new implementations that retained

24464-419: The relational model, the process of normalization led to such internal structures being replaced by data held in multiple tables, connected only by logical keys. For instance, a common use of a database system is to track information about users, their name, login information, various addresses and phone numbers. In the navigational approach, all of this data would be placed in a single variable-length record. In

24640-455: The relational/SQL model while aiming to match the high performance of NoSQL compared to commercially available relational DBMSs. The introduction of the term database coincided with the availability of direct-access storage (disks and drums) from the mid-1960s onwards. The term represented a contrast with the tape-based systems of the past, allowing shared interactive use rather than daily batch processing . The Oxford English Dictionary cites

24816-534: The relations and laws between them. Some of the main branches of modern number theory include elementary number theory , analytic number theory , algebraic number theory , and geometric number theory . Elementary number theory studies aspects of integers that can be investigated using elementary methods. Its topics include divisibility , factorization , and primality . Analytic number theory, by contrast, relies on techniques from analysis and calculus. It examines problems like how prime numbers are distributed and

24992-404: The result by using several one-digit operations in a row. For example, in the method addition with carries , the two numbers are written one above the other. Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to

25168-426: The right order ("Forward Referencing/Natural Order Calculation"). Pardo and Landau developed and implemented the software in 1969. LANPAR was used by Bell Canada, AT&T, and the 18 operating telephone companies nationwide for their local and national budgeting operations. LANPAR was also used by General Motors. Its uniqueness was Pardo's co-invention incorporating forward referencing/natural order calculation (one of

25344-406: The rightmost digit of the multiplicand and writing the result below, starting in the rightmost column. The same is done for each digit of the multiplicand and the result in each case is shifted one position to the left. As a final step, all the individual products are added to arrive at the total product of the two multi-digit numbers. Other techniques used for multiplication are the grid method and

25520-461: The rows and columns, then the formulas that defined each row or column. In 1975, Autotab-II was advertised as extending the original to a maximum of " 1,500 rows and columns, combined in any proportion the user requires... " GE Information Services, which operated the time-sharing service, also launched its own spreadsheet system, Financial Analysis Language (FAL), circa 1974. It was later supplemented by an additional spreadsheet language, TABOL, which

25696-415: The sake of clarity. Functionally, the spreadsheet operates as a whole and all cells operate as global variables within the spreadsheet (each variable having 'read' access only except its containing cell). A cell may contain a value or a formula , or it may simply be left empty. By convention, formulas usually begin with = sign. A value can be entered from the computer keyboard by directly typing into

25872-418: The same denominator then they can be added by adding their numerators and keeping the common denominator. For example, 2 7 + 3 7 = 5 7 {\displaystyle {\tfrac {2}{7}}+{\tfrac {3}{7}}={\tfrac {5}{7}}} . A similar procedure is used for subtraction. If the two numbers do not have the same denominator then they must be transformed to find

26048-623: The same problem. XML databases are a type of structured document-oriented database that allows querying based on XML document attributes. XML databases are mostly used in applications where the data is conveniently viewed as a collection of documents, with a structure that can vary from the very flexible to the highly rigid: examples include scientific articles, patents, tax filings, and personnel records. NoSQL databases are often very fast, do not require fixed table schemas, avoid join operations by storing denormalized data, and are designed to scale horizontally . In recent years, there has been

26224-437: The symbols I, V, X, L, C, D, M as its basic numerals to represent the numbers 1, 5, 10, 50, 100, 500, and 1000. A numeral system is positional if the position of a basic numeral in a compound expression determines its value. Positional numeral systems have a radix that acts as a multiplicand of the different positions. For each subsequent position, the radix is raised to a higher power. In the common decimal system, also called

26400-582: The technology progress in the areas of processors , computer memory , computer storage , and computer networks . The concept of a database was made possible by the emergence of direct access storage media such as magnetic disks , which became widely available in the mid-1960s; earlier systems relied on sequential storage of data on magnetic tape . The subsequent development of database technology can be divided into three eras based on data model or structure: navigational , SQL/ relational , and post-relational. The two main early navigational data models were

26576-477: The term "spread sheet" has been used in accounting to mean a grid of columns and rows in a ledger. And prior to the rise of computerized spreadsheets, "spread" referred to a newspaper or magazine item (text or graphics) that covers two facing pages, extending across the centerfold and treating the two pages as one large page. The compound word 'spread-sheet' came to mean the format used to present book-keeping ledgers—with columns for categories of expenditures across

26752-521: The time Lotus responded with usable Windows products, Microsoft had begun to assemble their Office suite. By 1995, Excel was the market leader, edging out Lotus 1-2-3, and in 2013, IBM discontinued Lotus 1-2-3 altogether. In 2006 Google launched their beta release Google Sheets , a web based spreadsheet application that can be accessed by multiple users from any device type using a compatible web browser, it can be used online and offline (with or without internet connectivity). Google Sheets originated from

26928-415: The time, PC World magazine called VisiCalc the first electronic spreadsheet. Bricklin has spoken of watching his university professor create a table of calculation results on a blackboard . When the professor found an error, he had to tediously erase and rewrite several sequential entries in the table, triggering Bricklin to think that he could replicate the process on a computer, using the blackboard as

27104-416: The top, invoices listed down the left margin, and the amount of each payment in the cell where its row and column intersect—which were, traditionally, a "spread" across facing pages of a bound ledger (book for keeping accounting records) or on oversized sheets of paper (termed 'analysis paper') ruled into rows and columns in that format and approximately twice as wide as ordinary paper. A batch "spreadsheet"

27280-423: The type(s) of computer they run on (from a server cluster to a mobile phone ), the query language (s) used to access the database (such as SQL or XQuery ), and their internal engineering, which affects performance, scalability , resilience, and security. The sizes, capabilities, and performance of databases and their respective DBMSs have grown in orders of magnitude. These performance increases were enabled by

27456-410: The underlying database model , with RDBMS for the relational , OODBMS for the object (oriented) and ORDBMS for the object–relational model . Other extensions can indicate some other characteristics, such as DDBMS for a distributed database management systems. The functionality provided by a DBMS can vary enormously. The core functionality is the storage, retrieval and update of data. Codd proposed

27632-455: The use of a "database management system" (DBMS), which is an integrated set of computer software that allows users to interact with one or more databases and provides access to all of the data contained in the database (although restrictions may exist that limit access to particular data). The DBMS provides various functions that allow entry, storage and retrieval of large quantities of information and provides ways to manage how that information

27808-460: The use of a "language" for data access , known as QUEL . Over time, INGRES moved to the emerging SQL standard. IBM itself did one test implementation of the relational model, PRTV , and a production one, Business System 12 , both now discontinued. Honeywell wrote MRDS for Multics , and now there are two new implementations: Alphora Dataphor and Rel. Most other DBMS implementations usually called relational are actually SQL DBMSs. In 1970,

27984-521: The user was assured that there were no remaining forward references within the spreadsheet. In 1968, three former employees from the General Electric computer company headquartered in Phoenix, Arizona set out to start their own software development house . A. Leroy Ellison, Harry N. Cantrell, and Russell E. Edwards found themselves doing a large number of calculations when making tables for

28160-476: The value 3 the result will be 15 . But C10 might also hold its formula referring to other cells, and so on. The ability to chain formulas together is what gives a spreadsheet its power. Many problems can be broken down into a series of individual mathematical steps, and these can be assigned to individual formulas in cells. Some of these formulas can apply to ranges as well, like the SUM function that adds up all

28336-443: Was ICL 's CAFS accelerator, a hardware disk controller with programmable search capabilities. In the long term, these efforts were generally unsuccessful because specialized database machines could not keep pace with the rapid development and progress of general-purpose computers. Thus most database systems nowadays are software systems running on general-purpose hardware, using general-purpose computer data storage. However, this idea

28512-538: Was a development of software written for the Apollo program on the System/360 . IMS was generally similar in concept to CODASYL, but used a strict hierarchy for its model of data navigation instead of CODASYL's network model. Both concepts later became known as navigational databases due to the way data was accessed: the term was popularized by Bachman's 1973 Turing Award presentation The Programmer as Navigator . IMS

28688-649: Was a spreadsheet application published by Sorcim in 1980, and originally bundled (along with WordStar) as part of the CP/M software package included with the Osborne 1 portable computer. It quickly became the de facto standard spreadsheet for CP/M. The introduction of Lotus 1-2-3 in November 1982 accelerated the acceptance of the IBM Personal Computer . It was written especially for IBM PC DOS and had improvements in speed and graphics compared to VisiCalc on

28864-412: Was also read and Mimer SQL was developed in the mid-1970s at Uppsala University . In 1984, this project was consolidated into an independent enterprise. Another data model, the entity–relationship model , emerged in 1976 and gained popularity for database design as it emphasized a more familiar description than the earlier relational model. Later on, entity–relationship constructs were retrofitted as

29040-475: Was called LANPAR — LANguage for Programming Arrays at Random. This was conceived and entirely developed in the summer of 1969, following Pardo and Landau's recent graduation from Harvard University. Co-inventor Rene Pardo recalls that he felt that one manager at Bell Canada should not have to depend on programmers to program and modify budgeting forms, and he thought of letting users type out forms in any order and having an electronic computer calculate results in

29216-735: Was developed by ancient Babylonians and had a radix of 60. Arithmetic operations are ways of combining, transforming, or manipulating numbers. They are functions that have numbers both as input and output. The most important operations in arithmetic are addition , subtraction , multiplication , and division . Further operations include exponentiation , extraction of roots , and logarithm . If these operations are performed on variables rather than numbers, they are sometimes referred to as algebraic operations . Two important concepts in relation to arithmetic operations are identity elements and inverse elements . The identity element or neutral element of an operation does not cause any change if it

29392-466: Was developed by an independent author, Oliver Vellacott in the UK. Both FAL and TABOL were integrated with GEIS's database system, DMS. The IBM Financial Planning and Control System was developed in 1976, by Brian Ingham at IBM Canada. It was implemented by IBM in at least 30 countries. It ran on an IBM mainframe and was the first application for financial planning developed with APL that completely hid

29568-403: Was different from programs like BASIC, C, FORTRAN, and COBOL in that a lot of the dirty work had already been done. The data manipulation is done by dBASE instead of by the user, so the user can concentrate on what he is doing, rather than having to mess with the dirty details of opening, reading, and closing files, and managing space allocation." dBASE was one of the top selling software titles in

29744-546: Was generally not successful. The main concepts are those of a grid of cells , called a sheet, with either raw data, called values, or formulas in the cells. Formulas say how to mechanically compute new values from existing values. Values are general numbers, but can also be pure text, dates, months, etc. Extensions of these concepts include logical spreadsheets. Various tools for programming sheets, visualizing data, remotely connecting sheets, displaying cells' dependencies, etc. are commonly provided. A "cell" can be thought of as

29920-560: Was implemented on an IBM 1130 and in 1963 was ported to an IBM 7040 by R. Brian Walsh at Marquette University , Wisconsin . This program was written in Fortran . Primitive timesharing was available on those machines. In 1968 BCL was ported by Walsh to the IBM 360 /67 timesharing machine at Washington State University . It was used to assist in the teaching of finance to business students. Students were able to take information prepared by

30096-543: Was launched 39 years ago in 1985. Notable current spreadsheet software: Discontinued spreadsheet software: Several companies have attempted to break into the spreadsheet market with programs based on very different paradigms. Lotus introduced what is likely the most successful example, Lotus Improv , which saw some commercial success, notably in the financial world where its powerful data mining capabilities remain well respected to this day. Spreadsheet 2000 attempted to dramatically simplify formula construction, but

30272-422: Was more interested in the difference in semantics: the use of explicit identifiers made it easier to define update operations with clean mathematical definitions, and it also enabled query operations to be defined in terms of the established discipline of first-order predicate calculus ; because these operations have clean mathematical properties, it becomes possible to rewrite queries in provably correct ways, which

30448-422: Was picked up by two people at Berkeley, Eugene Wong and Michael Stonebraker . They started a project known as INGRES using funding that had already been allocated for a geographical database project and student programmers to produce code. Beginning in 1973, INGRES delivered its first test products which were generally ready for widespread use in 1979. INGRES was similar to System R in a number of ways, including

30624-416: Was the first electronic spreadsheet on mainframe and time sharing computers. LANPAR was an acronym: LANguage for Programming Arrays at Random. VisiCalc (1979) was the first electronic spreadsheet on a microcomputer, and it helped turn the Apple II into a popular and widely used personal computer. Lotus 1-2-3 was the leading spreadsheet when DOS was the dominant operating system. Microsoft Excel now has

30800-490: Was to organize the data as a number of " tables ", each table being used for a different type of entity. Each table would contain a fixed number of columns containing the attributes of the entity. One or more columns of each table were designated as a primary key by which the rows of the table could be uniquely identified; cross-references between tables always used these primary keys, rather than disk addresses, and queries would join tables based on these key relationships, using

30976-552: Was used successfully for many years in developing such applications as financial and costing models for the US Congress and for Conrail . APLDOT was dubbed a "spreadsheet" because financial analysts and strategic planners used it to solve the same problems they addressed with paper spreadsheet pads. The concept of spreadsheets became widely known due to VisiCalc , developed for the Apple II in 1979 by VisiCorp staff Dan Bricklin and Bob Frankston . Significantly, it also turned

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