A logical operator denoting "if and only if" in mathematical proofs and logical statements, indicating logical equivalence.
Examples
Basic logical equivalence
x = 0 \iff x^2 = 0
Mathematical definition
\text{A triangle is equilateral} \iff \text{all sides have equal length}
Set theory equivalence
A = B \iff (x \in A \implies x \in B) \text{ and } (x \in B \implies x \in A)