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Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. This is a statement in the metalanguage, not the object language. The notation a ≡ b {\displaystyle a\equiv b} may occasionally be seen in physics, meaning the same as a := b {\displaystyle a:=b} .
Perpendicularity of lines in geometry; Orthogonality in linear algebra; Independence of random variables in probability theory; Coprimality in number theory; The double tack up symbol (тлл, U+2AEB in Unicode [1]) is a binary relation symbol used to represent: Conditional independence of random variables in probability theory [2]
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
As a matter of logical inference, to transpose or convert the terms of one proposition requires the conversion of the terms of the propositions on both sides of the biconditional relationship, meaning that transposing or converting (P → Q) to (Q → P) requires that the other proposition, (¬Q → ¬P), to be transposed or converted to (¬P ...
In geometry, the segment addition postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Logical equivalence is different from material equivalence. Formulas and are logically equivalent if and only if the statement of their material equivalence is a tautology.
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. [1]