Pure · Proof
Chapter 1 · 3
The idea
Disproof by counter-example
Disproving a universal ("for all") claim with a single example where it fails — shown with the arithmetic worked out. Why one counter-example is enough to disprove, why no number of supporting examples can prove, and where to hunt for the case that breaks a statement.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Proof
Disproof by counter-example
Disproving a universal ("for all") claim with a single example where it fails — shown with the arithmetic worked out. Why one counter-example is enough to disprove, why no number of supporting examples can prove, and where to hunt for the case that breaks a statement.
Why it works
One failure sinks a "for all"
" is prime for every positive integer ." Test it: gives , prime. gives , prime. It keeps working — for *forty straight values* — and it is still false. That asymmetry is this whole topic. A claim that says "for all …" is a promise about every case, so to disprove it you need just one case where it fails — a counter-example — while no mountain of working cases can ever prove it.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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