A bidirectional double-lined arrow symbol representing logical equivalence or biconditional statements in mathematical logic.
Examples
Logical not-if-and-only-if statement
A \nleftrightarrow B \text{ means 'A is not equivalent to B'}
Showing non-equivalence of expressions
x^2 + 1 = 0 \nleftrightarrow x = 1
Demonstrating distinct sets
\{x \in \mathbb{R} : x > 0\} \nleftrightarrow \{x \in \mathbb{R} : x \geq 0\}