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The colon, :, is a punctuation mark consisting of two equally sized dots aligned vertically. A colon often precedes an explanation, a list, [1] or a quoted sentence. [2] It is also used between hours and minutes in time, [1] between certain elements in medical journal citations, [3] between chapter and verse in Bible citations, [4] between a two numbers in a ratio, and, in the US, for ...
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...
The equals sign (British English) or equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality. [1] In an equation , it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value.
The vertical bar (or colon) is a separator that can be read as "such that", "for which", or "with the property that". The formula Φ(x) is said to be the rule or the predicate. All values of x for which the predicate holds (is true) belong to the set being defined.
According to Florian Cajori in A History of Mathematical Notations, Johann Rahn used both the therefore and because signs to mean "therefore"; in the German edition of Teutsche Algebra (1659) the therefore sign was prevalent with the modern meaning, but in the 1668 English edition Rahn used the because sign more often to mean "therefore".
Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true. The truth table of p EQ q (also written as p = q, p ↔ q, Epq, p ≡ q, or p == q) is as follows: The Venn diagram of A EQ B (red part is true)
The two most common representations for the copying assignment are equals sign (=) and colon-equals (:=). Both forms may semantically denote either an assignment statement or an assignment operator (which also has a value), depending on language and/or usage.
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (true or false). [1] [2] Truth values are used in computing as well as various types of logic.