Anti Pigeonhole Principle

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Revision as of 19:04, 21 December 2024 by Roshan (talk | contribs) (Created page with "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 pr...")

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The Anti Pigeonhole Principle is that if there are $n \in ℕ$ pigeons and $m \in 𝕄$ pigeonholes such that $n < m$ then there must be some pigeonholes that are empty.

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

Also, see Pigeonhole principle.

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