Search results
Results From The WOW.Com Content Network
IMPLY can be denoted in algebraic expressions with the logic symbol right-facing arrow (→). Logically, it is equivalent to material implication, and the logical expression ¬A v B. There are two symbols for IMPLY gates: the traditional symbol and the IEEE symbol. For more information see Logic gate symbols.
This article is supplemental for “Convergence of random variables” and provides proofs for selected results. Several results will be established using the portmanteau lemma: A sequence {X n} converges in distribution to X if and only if any of the following conditions are met:
We can use the results about convergence of the sequence of partial sums of the infinite series and apply them to the convergence of the infinite series itself. The Cauchy Criterion test is one such application. For any real sequence , the above results on convergence imply that the infinite series
Suppose we are given that .Then we have by the law of excluded middle [clarification needed] (i.e. either must be true, or must not be true).. Subsequently, since , can be replaced by in the statement, and thus it follows that (i.e. either must be true, or must not be true).
In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
Logical consequence (also entailment or logical implication), the relationship between statements that holds true when one logically "follows from" one or more others ...
In formal languages, truth functions are represented by unambiguous symbols.This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives.
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P.