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# Tag Archives: function

## Ways to prove a bijection

Posted in logic, proof
Tagged bijection, finite, function, injection, invertible, one-to-one, onto, proof, surjection
7 Comments

## One-sided inverses, surjections, and injections

Posted in logic
Tagged bijection, function, injection, invertible, one-to-one, onto, surjection
1 Comment

## Test your intuition: bijections

## A combinatorial proof: PIE a la mode!

Continuing from my last post in this series, we’re trying to show that , where is defined as which is what we get when we start with a sequence of consecutive th powers and repeatedly take successive differences. Recall that … Continue reading

Posted in arithmetic, combinatorics, proof
Tagged consecutive, difference, function, integers, matching, powers
Comments Off on A combinatorial proof: PIE a la mode!

## A combinatorial proof: counting bad functions

In a previous post we derived the following expression: . We are trying to show that , in order to show that starting with a sequence of consecutive th powers and repeatedly taking successive differences will always result in . … Continue reading

Posted in arithmetic, combinatorics, proof
Tagged consecutive, difference, function, integers, matching, powers
1 Comment

## A combinatorial proof: functions and matchings

We’re trying to prove the following equality (see my previous post for a recap of the story so far): In particular we’re trying to show that the two sides of this equation correspond to two different ways to count the … Continue reading

Posted in arithmetic, combinatorics, proof
Tagged consecutive, difference, function, integers, matching, powers
5 Comments

## Idempotent endofunctions

Via Topological Musings comes another neat little counting problem. A function is idempotent if applying it twice gives the same result as applying it once: that is, for any input x. Endofunction is just a fancy way of talking about … Continue reading