Logical Equivalence
Logical equivalence is an important concept in set-builder notation:
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This means that two sets are equal if and only if their "membership requirements" are logically equivalent.
For example, because, for any real number x, x2 = 1 if and only if |x| = 1; and, therefore, both constructions produce the same set {-1,1}.
Read more about this topic: Set-builder Notation
Famous quotes containing the word logical:
“It is possible—indeed possible even according to the old conception of logic—to give in advance a description of all ‘true’ logical propositions. Hence there can never be surprises in logic.”
—Ludwig Wittgenstein (1889–1951)