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ASMaths: PureAQARevision Notes1. Proof1.1 Proof1.1.3 Proof by Exhaustion

Proof by Exhaustion (AQA AS Maths: Pure)

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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 examplesProof by Exhaustion Notes Diagram_2, A Level & AS Level Pure Maths Revision Notes

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

Examiner Tip

  • 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

Proof by Exhaustion Example_2, A Level & AS Level Pure Maths Revision Notes

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    Previous:1.1.2 Proof by DeductionNext:1.1.4 Disproof by Counter Example
    Paul

    Author: Paul

    Expertise: Maths

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.