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

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Proof by Exhaustion
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Proof by exhaustion considers

Every possible case

Proof by exhaustion Step 1

Identify the statement to prove and possible cases

Proof by exhaustion Step 2

Break into finite distinct cases covering all scenarios

Proof by exhaustion Step 3

Prove statement for each case individually

Proof by exhaustion Step 4

Conclude statement is true for all cases

Single-digit odd numbers

1, 3, 5, 7, 9

Sum of two odd numbers is

Always even

Prove 47 prime by exhaustion: method

Check every possible factor for integer result

Upper limit when checking if nn is prime

Last integer less than n\sqrt{n}

Check 47 factors up to

6 (integer below 47\sqrt{47})

When checking primality, start at

2 (first prime number)

Why 47 is prime

All nn from 2 to 47\sqrt{47} are not factors

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