AQA A Level Maths: Pure复习笔记1.1.3 Proof by Exhaustion
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 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
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