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 edit summary |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 4: | Line 4: | ||
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.}} | |||
[[Category:Concepts]] | |||
[[Category:Jokes]] | |||
Latest revision as of 09:01, 5 December 2025
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.
