Proof by Exhaustion (AQA A-Level Mathematics): Flashcards

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Proof by Exhaustion
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Proof by exhaustion considers

Every possible case

Step 1 of proof by exhaustion

Identify statement and possible cases

Step 2 of proof by exhaustion

Break into finite distinct cases

Step 3 of proof by exhaustion

Prove statement for each case

Step 4 of proof by exhaustion

Conclude statement true for all cases

Single-digit odd numbers are

1,3,5,7,91, 3, 5, 7, 9

Sum of two odd numbers

Always even

When testing if nn is prime, check factors up to

Up to n\sqrt{n}

To prove 4747 is prime, check up to

47≈6\sqrt{47} \approx 6

Calculator method for testing 4747 prime: function

f(x)=47xf(x) = \frac{47}{x}

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Proof

Proof by Contradiction

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Proof

Proof by Contradiction

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Proof

Proof by Contradiction

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Proof

Proof by Contradiction

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