Anti Pigeonhole Principle: Difference between revisions
From Rest of What I Know
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..." |
(No difference)
|
Revision as of 19:04, 21 December 2024
The Anti Pigeonhole Principle is that if there are pigeons and pigeonholes such that then there must be some pigeonholes that are empty.
For sets and and function with where , then such that .
Also, see Pigeonhole principle.
