Misplaced Pages

#870129

45-401: The plural of formula can be either formulas (from the most common English plural noun form ) or, under the influence of scientific Latin , formulae (from the original Latin ). In mathematics , a formula generally refers to an equation or inequality relating one mathematical expression to another, with the most important ones being mathematical theorems . For example, determining

90-490: A Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false . A Boolean expression may be composed of a combination of the Boolean constants True/Yes or False/No , Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions . Boolean expressions correspond to propositional formulas in logic and are

135-409: A mathematical object , where as formulas denote a statement about mathematical objects. This is analogous to natural language, where a noun phrase refers to an object, and a whole sentence refers to a fact. For example, 8 x − 5 {\displaystyle 8x-5} is an expression, while 8 x − 5 ≥ 3 {\displaystyle 8x-5\geq 3}

180-425: A special case of Boolean circuits . Most programming languages have the Boolean operators OR , AND and NOT ; in C and some languages inspired by it , these are represented by "||" (double pipe character), "&&" (double ampersand ) and "!" ( exclamation point ) respectively, while the corresponding bitwise operations are represented by "|", "&" and "~" (tilde). In the mathematical literature

225-410: A bit string type and use BIT(1) rather than a separate Boolean type. In those languages the same operators serve for Boolean operations and bitwise operations. The languages represent OR, AND, NOT and EXCLUSIVE OR by "|", "&", "¬" (infix) and "¬" (prefix). Some programming languages, e.g., Ada , have short-circuit Boolean operators. These operators use a lazy evaluation , that is, if the value of

270-545: A cluster, but multiple Unix systems are usually Unices along the Latin model . The plural is sometimes formed by changing the vowel sound of the singular (these are sometimes called mutated plurals ): This group consists of words that historically belong to the Old English consonant declension, see Germanic umlaut § I-mutation in Old English . There are many compounds of man and woman that form their plurals in

315-531: A consonant usually drop the y and add -ies (pronounced /iz/ , or /aiz/ in words where the y is pronounced /ai/ ): Words ending in quy also follow this pattern, since in English qu is a digraph for two consonant sounds ( /kw/ ) or sometimes one ( /k/ ): However, proper nouns (particularly names of people) of this type usually form their plurals by simply adding -s : the two Kennedys , there are three Harrys in our office . With place names this rule

360-471: A form can often depend on context: for a scholar, the plural of appendix is appendices (following the original language); for some physicians, the plural of appendix is appendixes . Likewise, a radio or radar engineer works with antennas , but an entomologist deals with antennae . The choice of form can also depend on the level of discourse: traditional Latin plurals are found more often in academic and scientific contexts, whereas in daily speech

405-416: A formula typically describes a calculation , such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of a computer instruction such as. In computer spreadsheet software, a formula indicating how to compute the value of a cell , say A3 , could be written as where A1 and A2 refer to other cells (column A, row 1 or 2) within the spreadsheet. This

450-609: A full treatment, see Latin declensions .) Classical Greek has a simpler system, but still more complicated than that of English. Most loan words from Greek in English are from Attic Greek (the Athenian Greek of Plato , Aristotle , and other great writers), not Demotic Greek , Koine (Biblical) Greek , or Modern Greek . This is because Attic Greek is what is taught in classes in Greek in Western Europe, and therefore

495-562: A great many words from Classical Latin and Classical Greek . Classical Latin has a very complex system of endings in which there are five categories or declensions of nouns, adjectives, and pronouns (some with sub-categories). Usually, in borrowing words from Latin, the endings of the nominative are used: nouns whose nominative singular ends in -a ( first declension ) have plurals in -ae ( anima , animae ); nouns whose nominative singular ends in -um ( second declension neuter) have plurals in -a ( stadium , stadia ; datum , data ). (For

SECTION 10

#1732765618871

540-483: A key element and then assign numbers of atoms of the other elements in the compound—as ratios to the key element. For molecular compounds, these ratio numbers can always be expressed as whole numbers. For example, the empirical formula of ethanol may be written C 2 H 6 O, because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of ionic compounds, however, cannot be written as empirical formulas which contains only

585-444: A unary predicate symbol, and Q {\displaystyle Q} a ternary predicate symbol. In modern chemistry , a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound , using a single line of chemical element symbols , numbers , and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H 2 O

630-407: A voiced ending. In some words this voicing survives in the modern English plural. In the case of /f/ changing to /v/ , the mutation is indicated in the orthography as well; also, a silent e is added in this case if the singular does not already end with -e : In addition, there is one word where /s/ is voiced in the plural: Many nouns ending in /f/ or /θ/ (including all words where /f/

675-473: A wide range of other quantities in other disciplines. An example of a formula used in science is Boltzmann's entropy formula . In statistical thermodynamics , it is a probability equation relating the entropy S of an ideal gas to the quantity W , which is the number of microstates corresponding to a given macrostate : where k is the Boltzmann constant , equal to 1.380 649 × 10 J⋅K , and W

720-399: Is a formula. However, in some areas mathematics, and in particular in computer algebra , formulas are viewed as expressions that can be evaluated to true or false , depending on the values that are given to the variables occurring in the expressions. For example 8 x − 5 ≥ 3 {\displaystyle 8x-5\geq 3} takes the value false if x

765-415: Is a shortcut for the "paper" form A3 = A1+A2 , where A3 is, by convention, omitted because the result is always stored in the cell itself, making the stating of the name redundant. Formulas used in science almost always require a choice of units. Formulas are used to express relationships between various quantities, such as temperature, mass, or charge in physics; supply, profit, or demand in economics; or

810-426: Is a sibilant suffixed to the end of most nouns. Regular English plurals fall into three classes, depending upon the sound that ends the singular form: In English, there are six sibilant consonants: / s / , / z / , / ʃ / , / ʒ / , / tʃ / , and / dʒ / . When a singular noun ends in one of these sounds, its plural is spoken by appending /ɪz/ or /əz/ (in some transcription systems, this

855-405: Is abbreviated as /ᵻz/ ). The spelling adds -es , or -s if the singular already ends in -e : In most English varieties, there are five non-sibilant voiceless consonants that occur at the end of words: / p / , / t / , / k / , / f / , and / θ / ; some varieties also have / x / . When the singular form ends in a voiceless consonant other than a sibilant, the plural

900-447: Is given a value less than 1, and the value true otherwise. (See Boolean expression ) In mathematical logic , a formula (often referred to as a well-formed formula ) is an entity constructed using the symbols and formation rules of a given logical language . For example, in first-order logic , is a formula, provided that f {\displaystyle f} is a unary function symbol, P {\displaystyle P}

945-614: Is known. Here, notice that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic , analytical or in closed form . In a general context, formulas often represent mathematical models of real world phenomena, and as such can be used to provide solutions (or approximate solutions) to real world problems, with some being more general than others. For example,

SECTION 20

#1732765618871

990-425: Is normally formed by adding / s / (a voiceless sibilant). The spelling adds -s : Some that end in / f / or / θ / , however, are "near-regular". See section below. For a singular noun ending on a non-sibilant voiced consonant, the plural adds / z / (a voiced sibilant) and the spelling adds -s : In English, all vowels are voiced. Nouns ending in a vowel sound similarly add / z / to form

1035-411: Is not always adhered to: Sicilies and Scillies are the standard plurals of Sicily and Scilly , while Germanys and Germanies are both used. Nor does the rule apply to words that are merely capitalized common nouns: P&O Ferries (from ferry ). Other exceptions include lay-bys and stand-bys . Words ending in a y preceded by a vowel form their plurals by adding -s : However

1080-428: Is represented orthographically by gh or ph ) nevertheless retain the voiceless consonant: Some can do either: There are many other less regular ways of forming plurals, usually stemming from older forms of English or from foreign borrowings. Some nouns have identical singular and plural ( zero inflection). Many of these are the names of animals: As a general rule, game or other animals are often referred to in

1125-593: Is still considered incorrect in standard usage (see below ). Final -a becomes -ae (also -æ ), or just adds -s : Scientific abbreviations for words of Latin origin ending in -a , such as SN for supernova , can form a plural by adding -e , as SNe for supernovae . Final -ex or -ix becomes -ices (pronounced /ᵻsiːz/ ), or just adds -es : Final -is becomes -es (pronounced /iːz/ ) or -ises/-ides : Except for words derived from Greek polis , which become poleis (pronounced /iːs/ or /iːz/ ): Boolean expression In computer science ,

1170-452: Is the chemical formula for water , specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O 3 denotes an ozone molecule consisting of three oxygen atoms and a net negative charge . A chemical formula identifies each constituent element by its chemical symbol , and indicates the proportionate number of atoms of each element. In empirical formulas , these proportions begin with

1215-635: Is the number of microstates consistent with the given macrostate . English plurals#Regular plurals English plurals include the plural forms of English nouns and English determiners . This article discusses the variety of ways in which English plurals are formed from the corresponding singular forms, as well as various issues concerning the usage of singulars and plurals in English. For plurals of pronouns, see English personal pronouns . Phonological transcriptions provided in this article are for Received Pronunciation and General American . For more information, see English phonology . Although

1260-418: The volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion . However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: Having obtained this result, the volume of any sphere can be computed as long as its radius

1305-599: The Anglicised forms are more common. In the following table, the Latin plurals are listed, together with the Anglicised forms when these are more common. Different paradigms of Latin pronunciation can lead to confusion as to the number or gender of the noun in question. As traditionally used in English, including scientific, medical, and legal contexts, Latin nouns retain the classical inflection with regard to spelling; however those inflections use an Anglicised pronunciation :

1350-624: The entomologist pronounces antennae as /ænˈtɛni/ . This may cause confusion for those familiar with the Classical Latin pronunciation /ænˈtɛnaɪ/ . The words alumni (masculine plural) and alumnae (feminine plural) are notorious in this regard, as alumni in Anglicised pronunciation sounds the same as alumnae in Classical Latin pronunciation , and vice versa . Because many of these plurals do not end in -s , some of them have been reinterpreted as singular forms: particularly

1395-529: The everyday meaning of plural is "more than one", the grammatical term has a slightly different technical meaning. In the English system of grammatical number, singular means "one (or minus one)", and plural means "not singular". In other words, plural means not just "more than one" but also "less than one (except minus one)". This less-than aspect can be seen in cases like the temperature is zero degrees (not * zero degree ) and 0.5 children per woman (not * 0.5 child per woman ). The plural morpheme in English

Formula - Misplaced Pages Continue

1440-506: The formula is an expression of Newton's second law , and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay , may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations. Expressions are distinct from formulas in the sense that they don't usually contain relations like equality (=) or inequality (<). Expressions denote

1485-716: The name of the London parish of Clerkenwell , which derives its name from being the Clerks' Well associated with the Clerkenwell Priory of the Knights Hospitaller . The following -(e)n plurals are found in dialectal, rare, or archaic usage: The word box , referring to a computer, is occasionally pluralized humorously to boxen in the hacker subculture. In the same context, multiple VAX computers are sometimes called Vaxen particularly if operating as

1530-460: The number of atoms to reflect those in the molecule, so that the molecular formula for glucose is C 6 H 12 O 6 rather than the glucose empirical formula, which is CH 2 O. Except for the very simple substances, molecular chemical formulas generally lack needed structural information, and might even be ambiguous in occasions. A structural formula is a drawing that shows the location of each atom, and which atoms it binds to. In computing ,

1575-423: The plural form (rarely used) of money is usually monies , although moneys is also found. Also, the plural of trolley can be either trolleys or trollies , although the former is more common. Nouns written with -i usually have plurals in -is but some in -ies are also found. In Old and Middle English, voiceless fricatives /f/ and /θ/ mutated to voiced fricatives /v/ and /ð/ respectively before

1620-536: The plural, although many people are not aware of this rule; see § Irregular plurals from other languages below. The plurals of a few nouns are formed from the singular by adding -n or -en , stemming from the Old English weak declension. Only the following three are commonly found: As noted, the word "children" comes from an earlier form "childer". There were formerly a few other words like this: eyre/eyren (eggs), lamber/lambren (lambs), and calver/calveren (calves). An interesting example may be found embedded in

1665-405: The plural. The spelling usually adds -s , but certain instances (detailed below) may add -es instead: Singular nouns ending in o preceded by a consonant in many cases spell the plural by adding -es (pronounced / z / ): However many nouns of foreign origin, including almost all Italian loanwords, add only -s : Nouns ending in a vocalic y (that is, used as a vowel ) preceded by

1710-443: The same way: postmen , policewomen , etc. The plural of mongoose is mongooses or sometimes mongeese . Mongeese is a back-formation by analogy to goose / geese and is often used in a jocular context. The form meese is sometimes also used humorously as the plural of moose —normally moose or mooses —or even of mouse . Some words have irregular plurals that do not fit any of the types given here. English has borrowed

1755-559: The singular for the plural in a sporting context: "He shot six brace of pheasant", "Carruthers bagged a dozen tiger last year", whereas in another context such as zoology or tourism the regular plural would be used. Eric Partridge refers to these sporting terms as "snob plurals" and conjectures that they may have developed by analogy with the common English irregular plural animal words "deer", "sheep" and "trout". Similarly, nearly all kinds of fish have no separate plural form (though there are exceptions—such as rays, sharks or lampreys). As to

1800-750: The singular. Other nouns that have identical singular and plural forms include: Many names for Native American peoples are not inflected in the plural: Exceptions include Algonquins , Apaches , Aztecs , Chippewas , Hurons , Incas , Mohawks , Oneidas , and Seminoles . English sometimes distinguishes between regular plural forms of demonyms / ethnonyms (e.g. "five Dutchmen", "several Irishmen"), and uncountable plurals used to refer to entire nationalities collectively (e.g. "the Dutch", "the Irish"). Certain other words borrowed from foreign languages such as Japanese and Māori are "correctly" not inflected in

1845-400: The symbols used are often "+" ( plus ), " · " ( dot ) and overbar , or "∨" ( vel ), "∧" ( et ) and "¬" ( not ) or "′" (prime). Some languages, e.g., Perl and Ruby , have two sets of Boolean operators, with identical functions but different precedence. Typically these languages use and , or and not for the lower precedence operators. Some programming languages derived from PL/I have

Formula - Misplaced Pages Continue

1890-442: The whole numbers. An example is boron carbide , whose formula of CB n is a variable non-whole number ratio, with n ranging from over 4 to more than 6.5. When the chemical compound of the formula consists of simple molecules , chemical formulas often employ ways to suggest the structure of the molecule. There are several types of these formulas, including molecular formulas and condensed formulas . A molecular formula enumerates

1935-515: The word fish itself, the plural is usually identical to the singular, although fishes is sometimes used, especially when meaning "species of fish". Fishes is also used in iconic contexts, such as the Bible story of the loaves and fishes , or the reference in The Godfather , "Luca Brasi sleeps with the fishes." The plurals of the names of fishes either take the ending -s or is the same as

1980-485: The words datum and medium (as in a "medium of communication"), where the original plurals data and media are now, in many contexts, used by some as singular mass nouns: "The media is biased"; "This data shows us that ..." (although a number of scientists, especially of British origin, still say "These data show us that ..."). See below for more information. Similarly, words such as criteria and phenomena are used as singular by some speakers, although this

2025-446: Was the Greek that the word borrowers knew. The general trend with loanwords is toward what is called Anglicisation or naturalisation , that is, the re-formation of the word and its inflections as normal English words. Many nouns have settled on, or acquired a modern form from the original (usually Latin). Other nouns have become Anglicised, taking on the normal "s" ending. In some cases, both forms are still competing. The choice of

#870129