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If $A\Rightarrow B$ and $B\Rightarrow A$ (i.e, $A\Rightarrow B\wedge B\Rightarrow A$, where $\Rightarrow $ denotes Implies), then $A$ and $B$ are said to be equivalent, a relationship which is written symbolically as $A\Leftrightarrow B$ or $A\rightleftharpoons
B$. However, if $A$ and $B$ are ``equivalent by definition'' (i.e., $A$ is Defined to be $B$), this is written $A\equiv B$, a notation which conflicts with that for a Congruence.

See also Defined, Iff, Implies

© 1996-9 Eric W. Weisstein