Anti Pigeonhole Principle: Difference between revisions
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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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Also, see [[wikipedia:Pigeonhole principle|Pigeonhole principle]]. | Also, see [[wikipedia:Pigeonhole principle|Pigeonhole principle]]. | ||
== Examples == | |||
Suppose <math>$x</math> is allocated to healthcare and some treatment costs <math>$y</math> then there are <math>$x/$y</math> times that the treatment can be administered. After that, everyone else goes without treatment. If insurance denies no one, then that means that the first <math>$x/$y</math> people get the treatment and no one else does. | |||
Latest revision as of 20:28, 22 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.
Examples[edit]
Suppose is allocated to healthcare and some treatment costs then there are times that the treatment can be administered. After that, everyone else goes without treatment. If insurance denies no one, then that means that the first people get the treatment and no one else does.
