In mathematics, "iff" stands for "if and only if".

$$P \iff Q$$

In mathematics, "iff" stands for "if and only if". It is a logical connector that indicates a biconditional statement, meaning that both directions of implication hold true.

Formally, a statement of the form:
$$P \iff Q$$
means that:

1. If $P$ is true, then $Q$ is also true.
2. If $Q$ is true, then $P$ is also true.

This can be written as:
$$(P \Rightarrow Q) \text{ and } (Q \Rightarrow P).$$

Example

• The statement:
  $$A \text{ is a square matrix } \iff A \text{ has the same number of rows and columns}$$
  means that:
  • If $A$ is a square matrix, then it has the same number of rows and columns.
  • If $A$ has the same number of rows and columns, then it is a square matrix.

The "iff" condition ensures that the two statements are equivalent: one is true if and only if the other is also true.