Edexcel A Level Maths: Pure:复习笔记1.1.3 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