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The phrase "'''if and only if'''"
&mdash; in print often abbreviated to "'''iff'''" &mdash;
is frequently used in mathematical language
to express that two statements are (logically) equivalent,
i.e., that they imply each other.
Thus it has the same meaning as the phrase
"[[necessary and sufficient]]".

In mathematical formulae "if and only if" is written as
"<math>\Leftrightarrow</math>".

'''Examples''':

* Three versions of the same statement (A product is not 0 unless a factor is.)
:*  The product of two (real) numbers is 0 if and only if one of the two factors equals 0. 
:* ''ab'' = 0 iff ''a'' = 0 or ''b'' = 0.
:* <math> ab=0 \Leftrightarrow a=0 \text{ or } b=0  </math>

*  A monotone sequence of real numbers is convergent iff it is bounded.