A-Level Mathematics · Proof · A3

Proof by exhaustion.

Prove a statement by checking every possible case in a finite, complete list.

A3 Proof9 MinutesAnimated lesson

WATCH THE IDEA MOVE

Animated
explanation.

Pause, replay and follow every logical step at your own pace.

01 / KEY IDEA

Exhaustion is valid only when the cases are finite and together cover every possibility.

02 / LEARNING OUTCOMES
  • Identify all possible cases
  • Check each case correctly
  • Explain why the list is complete

WORKED EXAMPLE

Follow every
reason.

Show that n² + n is even for n modulo 2.

01

Every integer is either even or odd.

02

If n is even, n² + n is even + even. If n is odd, n² + n is odd + odd.

03

Both cases give an even result, and the cases exhaust all integers.

QUICK CHECK

Test the
logic.

Choose the statement that describes a valid mathematical proof.

What makes a mathematical proof valid?