Proof by Exhaustion (Edexcel IAL Maths)

Spec point — 1.2

Proof by exhaustion

What is proof by exhaustion?

• Proof by exhaustion is a way to show that the desired result works for every allowed value

How do I prove a result by exhaustion?

• Using proof by exhaustion means testing every allowed value not just showing a few examples

Difficulties with proof by exhaustion

• In many cases proof by exhaustion is not practical, or possible

  • Proving all multiples of 4 are even can’t be shown for every multiple of 4

• Aim to minimise the work involved

  • Proving a number is prime only requires testing factors up to the square root

Exam Hint

• Try a simpler case if you are stuck.
• For example, if you are asked to prove that 97 is a prime number you could try thinking about what you would do for smaller primes such as 7 or 11.

Worked Example