Building Bridges of Logic

Intro to Proofs · Axiom Academy

A proof is like a bridge across a gap: each logical step is a plank, and every plank has to connect — or the whole thing falls into the chasm. The logical chasm — and the bridge across it In mathematics you start with a hypothesis (what you know) and have to reach a conclusion (what you want to prove). Between them sits a gap. You can't just leap across — you build a bridge, one justified step at a time, until the two sides connect. Watch the bridge build itself. Starting from “n is even” , each plank is one logical step that follows from the one before it, laid across the chasm until it lands on “n² is even.” When the last plank connects, the proof is complete. A proof isn't magic — it's a path. Each plank is a step that must hold its own weight and connect to its neighbours. Prove it yourself: if n is even, then n² is even. Drag each logic plank from the tray onto a slot so the chain reads in order from the hypothesis to the conclusion. Drop a plank back to the tray (or hit Reset) to rearrange. Drag a plank onto a slot. To change your mind, drag a placed plank to another slot or back here. This is a direct proof: start from the definition of “even” (n = 2k), do valid algebra, and land on the definition of “even” again — n² = 2·(something).

This is the written version of the interactive lesson above. See the full Intro to Proofs course.