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29-518: (Redirected from B-Series ) B series may refer to: B series , a term in philosophy introduced by John McTaggart B-series , a type of power series in numerical analysis introduced by John C. Butcher BMC B-series engine , a type of combustion engine Cummins B Series engine , a family of diesel engines Chevrolet/GMC B series , a bus Series B , venture capital funding round Series B banknotes , Irish banknotes Transperth B-series train ,

58-404: A logarithm of the geometric mean is the arithmetic mean of the logarithms of its n arguments From a mathematical point of view, a function of n arguments can always be considered as a function of a single argument that is an element of some product space . However, it may be convenient for notation to consider n -ary functions, as for example multilinear maps (which are not linear maps on

87-399: A different series of temporal positions by way of two-term relations that are asymmetric , irreflexive and transitive (forming a strict partial order ): "earlier than" (or precedes) and "later than" (or follows). An important difference between the two series is that while events continuously change their position in the A series, their position in the B series does not. If an event ever

116-755: A ternary operator, */ , which multiplies the first two (one-cell) numbers, dividing by the third, with the intermediate result being a double cell number. This is used when the intermediate result would overflow a single cell. The Unix dc calculator has several ternary operators, such as | , which will pop three values from the stack and efficiently compute x y mod z {\textstyle x^{y}{\bmod {z}}} with arbitrary precision . Many ( RISC ) assembly language instructions are ternary (as opposed to only two operands specified in CISC); or higher, such as MOV %AX , ( %BX , %CX ) , which will load ( MOV ) into register AX

145-462: A type of electric multiple unit used by Transperth Trains in Perth, Western Australia See also [ edit ] B class (disambiguation) A series (disambiguation) C series (disambiguation) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title B series . If an internal link led you here, you may wish to change

174-476: A variable number of arguments are called multigrade , anadic, or variably polyadic. Latinate names are commonly used for specific arities, primarily based on Latin distributive numbers meaning "in group of n ", though some are based on Latin cardinal numbers or ordinal numbers . For example, 1-ary is based on cardinal unus , rather than from distributive singulī that would result in singulary . n - ary means having n operands (or parameters), but

203-500: Is combined with the -ary suffix. For example: A constant can be treated as the output of an operation of arity 0, called a nullary operation . Also, outside of functional programming , a function without arguments can be meaningful and not necessarily constant (due to side effects ). Such functions may have some hidden input , such as global variables or the whole state of the system (time, free memory, etc.). Examples of unary operators in mathematics and in programming include

232-461: Is dynamic and ephemeral , in a state of constant flux, as in his famous statement that it is impossible to step twice into the same river (since the river is flowing). McTaggart distinguished the ancient conceptions as a set of relations. According to McTaggart, there are two distinct modes in which all events can be ordered in time. In the first mode, events are ordered as future , present , and past . Futurity and pastness allow of degrees, while

261-421: Is earlier than some events and later than the rest, it is always earlier than and later than those very events. Furthermore, while events acquire their A series determinations through a relation to something outside of time, their B series determinations hold between the events that constitutes the B series. This is the B series, and the philosophy that says all truths about time can be reduced to B series statements

290-513: Is often used as a synonym of "polyadic". These words are often used to describe anything related to that number (e.g., undenary chess is a chess variant with an 11×11 board, or the Millenary Petition of 1603). The arity of a relation (or predicate ) is the dimension of the domain in the corresponding Cartesian product . (A function of arity n thus has arity n +1 considered as a relation.) In computer programming , there

319-401: Is popularly believed that he treated tenses as monadic properties. Later philosophers have independently inferred that McTaggart must have understood tense as monadic because English tenses are normally expressed by the non-relational singular predicates "is past", "is present" and "is future", as noted by R. D. Ingthorsson. From a second point of view, events can be ordered according to

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348-488: Is the B-theory of time . The logic and the linguistic expression of the two series are radically different. The A series is tensed and the B series is tenseless . For example, the assertion "today it is raining" is a tensed assertion because it depends on the temporal perspective—the present—of the person who utters it, while the assertion "It rained on 22 November 2024" is tenseless because it does not so depend. From

377-486: Is the number of arguments or operands taken by a function , operation or relation . In mathematics, arity may also be called rank, but this word can have many other meanings. In logic and philosophy , arity may also be called adicity and degree . In linguistics , it is usually named valency . In general, functions or operators with a given arity follow the naming conventions of n -based numeral systems , such as binary and hexadecimal . A Latin prefix

406-425: The geometric mean of n positive real numbers is an n -ary function: ( ∏ i = 1 n a i ) 1 n =   a 1 a 2 ⋯ a n n . {\displaystyle \left(\prod _{i=1}^{n}a_{i}\right)^{\frac {1}{n}}=\ {\sqrt[{n}]{a_{1}a_{2}\cdots a_{n}}}.} Note that

435-443: The logarithm operator, the addition operator, and the division operator. Logical predicates such as OR , XOR , AND , IMP are typically used as binary operators with two distinct operands. In CISC architectures, it is common to have two source operands (and store result in one of them). The computer programming language C and its various descendants (including C++ , C# , Java , Julia , Perl , and others) provide

464-439: The ternary conditional operator ?: . The first operand (the condition) is evaluated, and if it is true, the result of the entire expression is the value of the second operand, otherwise it is the value of the third operand. The Python language has a ternary conditional expression, x if C else y . In Elixir the equivalent would be, if ( C , do : x , else : y ) . The Forth language also contains

493-555: The two's complement , address reference , and the logical NOT operators are examples of unary operators. All functions in lambda calculus and in some functional programming languages (especially those descended from ML ) are technically unary, but see n-ary below. According to Quine , the Latin distributives being singuli , bini , terni , and so forth, the term "singulary" is the correct adjective, rather than "unary". Abraham Robinson follows Quine's usage. In philosophy,

522-440: The unary minus and plus, the increment and decrement operators in C -style languages (not in logical languages), and the successor , factorial , reciprocal , floor , ceiling , fractional part , sign , absolute value , square root (the principal square root), complex conjugate (unary of "one" complex number , that however has two parts at a lower level of abstraction), and norm functions in mathematics. In programming

551-612: The B-theory include eternalism and four-dimensionalism . Vincent Conitzer argues that A-theory is related to Benj Hellie's vertiginous question and Caspar Hare's ideas of egocentric presentism and perspectival realism . He argues that A-theory being true and "now" being metaphysically distinguished from other moments of time implies that the "I" is also metaphysically distinguished from other first-person perspectives. Arity#Unary In logic , mathematics , and computer science , arity ( / ˈ ær ɪ t i / )

580-402: The adjective monadic is sometimes used to describe a one-place relation such as 'is square-shaped' as opposed to a two-place relation such as 'is the sister of'. Most operators encountered in programming and mathematics are of the binary form. For both programming and mathematics, these include the multiplication operator , the radix operator, the often omitted exponentiation operator,

609-572: The contents of a calculated memory location that is the sum (parenthesis) of the registers BX and CX . The arithmetic mean of n real numbers is an n -ary function: x ¯ = 1 n ( ∑ i = 1 n x i ) = x 1 + x 2 + ⋯ + x n n {\displaystyle {\bar {x}}={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)={\frac {x_{1}+x_{2}+\dots +x_{n}}{n}}} Similarly,

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638-439: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=B_series&oldid=1189643181 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages A series and B series John McTaggart introduced these terms in 1908, in an argument for

667-421: The other hand, the character of being "past, present or future" of the events "E" or "F" does change with time. In the image of McTaggart the passage of time consists in the fact that terms ever further in the future pass into the present...or that the present advances toward terms ever farther in the future. If we assume the first point of view, we speak as if the B series slides along a fixed A series. If we assume

696-404: The point of view of their truth-values , the two propositions are identical (both true or both false) if the first assertion is made on 22 November 2024. The non-temporal relation of precedence between two events, say "E precedes F", does not change over time (excluding from this discussion the issue of the relativity of temporal order of causally disconnected events in the theory of relativity). On

725-418: The present does not. When we speak of time in this way, we are speaking in terms of a series of positions which run from the remote past through the recent past to the present, and from the present through the near future all the way to the remote future. The essential characteristic of this descriptive modality is that one must think of the series of temporal positions as being in continual transformation , in

754-449: The product space, if n ≠ 1 ). The same is true for programming languages, where functions taking several arguments could always be defined as functions taking a single argument of some composite type such as a tuple , or in languages with higher-order functions , by currying . In computer science, a function that accepts a variable number of arguments is called variadic . In logic and philosophy, predicates or relations accepting

783-499: The second point of view, we speak as if the A series slides along a fixed B series. There are two principal varieties of the A-theory, presentism and the growing block universe . Both assume an objective present, but presentism assumes that only present objects exist, while the growing block universe assumes both present and past objects exist, but not future ones. Views that assume no objective present and are therefore versions of

812-499: The sense that an event is first part of the future, then part of the present, and then part of the past. Moreover, the assertions made according to this modality correspond to the temporal perspective of the person who utters them. This is the A series of temporal events. Although originally McTaggart defined tenses as relational qualities, i.e. qualities that events possess by standing in a certain relations to something outside of time (that does not change its position in time), today it

841-404: The unreality of time . They are now commonly used by contemporary philosophers of time . Metaphysical debate about temporal orderings reaches back to the ancient Greek philosophers Heraclitus and Parmenides . Parmenides thought that reality is timeless and unchanging. Heraclitus, in contrast, believed that the world is a process of ceaseless change , flux and decay. Reality for Heraclitus

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