Explain the difference between an axiom, a conjecture and a theorem. Also give examples of each.

An axiom, a conjecture, and a theorem are terms used in mathematics to describe different types of mathematical statements. Here's an explanation of each term along with examples:

1. Axiom: An axiom is a statement or proposition that is considered to be self-evident or universally accepted without the need for proof. Axioms serve as the foundational principles or assumptions upon which an entire mathematical system or theory is built. They are considered to be true and are used as starting points for deriving other mathematical results. Axioms are not proven within the system itself but are accepted as fundamental truths.

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