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Proof Techniques Basics

Learn core proof patterns

This guide introduces common proof techniques and how to choose among them: direct proof for constructive arguments, contrapositive/contradiction for logical structure, and induction for statements over integers.

Direct proof

Start from assumptions and apply definitions/known results step-by-step until the conclusion follows.

Contrapositive and contradiction

Rewrite implications or assume the opposite to expose a logical conflict.

Induction

Prove a base case, assume n, then show n+1; be explicit about the inductive hypothesis.

Write cleanly

State assumptions, define symbols, and end with a clear conclusion so the argument is easy to follow.

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