28 lines
942 B
Markdown
28 lines
942 B
Markdown
# 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]]
|