proof

Proof is what settles a question — the evidence or the working that leaves nothing left to argue about. A receipt is proof you paid. A passport is proof of who you are. In maths, a proof is the chain of steps showing a statement cannot be any other way.

The word lives on of: proof of purchase, proof of address, proof of identity. In that use it does not count — you have some proof, or none, but never a proof — while in mathematics and logic a proof is a countable thing you write out and hand in. Proof also works on the end of other words, meaning able to keep something out: waterproof, soundproof, bulletproof, childproof. In printing, a proof is the trial copy read for mistakes, which is where proofread comes from. And mind the pair: you prove a thing with a v, and what you end up holding is proof with an f.

Phrases it lives in

• the proof of the pudding is in the eating — you only find out whether something works by trying it
• burden of proof — the duty to prove the case, which falls on whoever makes the claim
• living proof — a person whose existence shows the thing is possible