> ## Documentation Index
> Fetch the complete documentation index at: https://math.aboneda.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Introduction to Proof

> Proof techniques and mathematical reasoning

# Proof

Mathematical proof is a rigorous argument that establishes the truth of a statement beyond any doubt. Learning to read and write proofs is central to all advanced mathematics.

## Key Topics

* **Direct Proof** — assuming premises and deriving the conclusion step by step
* **Proof by Contradiction** — assuming the negation and reaching a contradiction
* **Proof by Contrapositive** — proving the contrapositive of an implication
* **Mathematical Induction** — base case + inductive step for statements over natural numbers
* **Strong Induction** — using all preceding cases in the inductive step
* **Proof by Cases** — exhaustively covering all possibilities
* **Existence & Uniqueness Proofs** — constructive and non-constructive approaches
* **Diagonalization** — Cantor's technique for uncountability and beyond