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logic-proofs/01-what-is-a-proof.md

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+# What is a Proof?
+
+**Source:** MIT 6.1200J Lecture 01
+
+## Definition
+A **mathematical proof** is a verification of a proposition by a chain of logical deductions from a base set of axioms.
+
+## Key Components
+1. **Proposition** — A statement that is either True or False
+2. **Axioms** — Assumed-to-be-true base statements
+3. **Logical deductions** — Chain of reasoning connecting axioms to conclusion
+
+## Important: Different Proof Contexts
+- Physics: Experiment/observation
+- Statistics: Sampling
+- Law: Judge/jury verdict
+- Business: Authority
+- Mathematics: Logical deduction from axioms
+
+## Why State Axioms?
+- Mathematics requires assumptions (axiom = stated assumption)
+- Different axiom systems lead to different mathematical worlds
+- Example: Euclidean vs. Hyperbolic geometry — both valid with different parallel axioms
+
+## Related
+- [[../discrete-math/00-index|Discrete Math Foundations]]
+- [[02-propositions|Propositions]]