- Axioms or POSTULATES: Statement that is self-evidently true even without proof.
- DEFINITION: Statement that gives precise meaning to a concept or word.
- Conjectures: Statement that has not yet been proved or disproved.
- PROOF: Sequence of rigorous mathematical arguments in clear and concise fashion. Represents absolute truth vs. empirical proof.
- Theorems: Any math statement that can be shown as true using accepted logical or mathematical arguments. Corollary, Proposition, Lemma.
Axioms and Theorems are both considered true. Their only difference is that axioms are self-evidently true while theorems must have proof through logical and mathematical arguments.
