Editing Anti Pigeonhole Principle

The [[Anti Pigeonhole Principle]] is that if there are <math>n \in \mathbb{N}</math> pigeons and <math>m \in \mathbb{M}</math> pigeonholes such that <math>n < m</math> then there must be some pigeonholes that are empty.

For sets <math>A</math> and <math>B</math> and function <math>f: A \to B</math> with <math>|A| = n ; |B| = m</math> where <math>n < m</math>, then <math>\exists b \in B</math> such that <math>|f^{-1}({b})| = 0</math>.

Also, see [[wikipedia:Pigeonhole principle|Pigeonhole principle]].