Pure · Proof
Chapter 1 · 3
The idea
Proof by exhaustion
Proving a statement by splitting it into a finite, complete set of cases and checking every one — either a short list of values, or all integers split by parity or remainder. Why the cases must leave no gaps, and why exhaustion only works when the cases really are finite.
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Pure · Proof
Proof by exhaustion
Proving a statement by splitting it into a finite, complete set of cases and checking every one — either a short list of values, or all integers split by parity or remainder. Why the cases must leave no gaps, and why exhaustion only works when the cases really are finite.
Why it works
Check every case — when the cases are finite
You cannot check infinitely many numbers one by one — but sometimes you don't have to, because the claim splits into a handful of doors, and opening every door is itself a proof. Some statements break into a finite number of cases; check every case and the statement is proved — that is proof by exhaustion. It comes in two shapes. The first is a short list of values: "for , , …" gives only the values — test each.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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