Difference between a theorem, a lemma, and a proposition
A statement assumed to be true without proof.
A minor result whose sole purpose is to help to proof a theorem. It is a stepping stone to reach a theorem.
A mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, or book the term theorem is generally reserved for the most important results.
A result whose proof relies heavily on a given theorem.
A proved and often interesting result, but generally less important than a theorem.
A statement that is unproved, but is believed to be true.
An assertion that is then proved. It is often used like an informal lemma.
A statement that can be shown to be both true and false. Paradoxes are often used to show the inconsistencies in a flawed theory .