**Proofs** are a finite sequence of claims that aim to show the truthfulness or falsehood of a statement.

**Tools:**

- Axioms
- Definitions
- Theorems
- Propositions
- Postulates
- Facts

**Ways**:

*Direct Proofs*: Proofs where the truthfulness or falsehood of a statement is reached by a direct combination of established facts, theorems, and axioms*Induction Proofs*:- Prove it for the base case
- Assume it is true for
- Then prove it for

- Prove it for the base case
- Contrapositive Proofs
- Exhaustion Proofs
- Construction Proofs