Dirichlet's Box Principle/Corollary
Jump to navigation Jump to search
Corollary to Dirichlet's Box Principle
A direct application of the Dirichlet's Box Principle.
- Suppose you have $n + 1$ pigeons, but have only $n$ holes for them to stay in.
- By the pigeonhole principle, at least one of the holes houses $2$ pigeons.
It is also known as (Dirichlet's) drawer (or shelf) principle.
Some sources give it as the letterbox principle or letter-box principle.
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.6$: Theorem $9$
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.18$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): pigeonhole principle
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): pigeonhole principle
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Pigeonhole Principle
- Weisstein, Eric W. "Dirichlet's Box Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletsBoxPrinciple.html