Proof

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:
  1. Prove it for the base case
  2. Assume it is true for
  3. Then prove it for
• Contrapositive Proofs
• Exhaustion Proofs
• Construction Proofs