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.
{{#seo:|description=The Anti Pigeonhole Principle states that if there are fewer pigeons than pigeonholes, then some pigeonholes must be empty.}}
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Latest revision as of 09:01, 5 December 2025

The Anti Pigeonhole Principle is that if there are n pigeons and m𝕄 pigeonholes such that n<m then there must be some pigeonholes that are empty.

For sets A and B and function f:AB with |A|=n;|B|=m where n<m, then bB such that |f1(b)|=0.

Also, see Pigeonhole principle.

Examples[edit]

Suppose $x is allocated to healthcare and some treatment costs $y then there are $x/$y 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 $x/$y people get the treatment and no one else does.