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**Definition:** A precise and unambiguous description of the meaning of a mathematical term. (Everybody knows that…)
**Claim:**Assertion that is then proved. It is often used like an informal **lemma**. (I say…)
**Axiom**/**Postulate: ****A **statement that is assumed to be true without proof. (Believe me when I say…)
**Lemma:** A lemma is a useful **observation** that serves as a stepping stone to understand** theorems**. (I see…)
**Conjecture**: A conjecture is a guess mostly based on **observations**. (I guess…)
**Hypothesis**: A hypothesis is a** conjecture** with lots of partial evidences and significant consequences. (I believe…)
**Theorem**: A theorem is a single essential contribution to a **theory** (I know…)
**Corollary**: A result in which the (usually short) proof relies heavily on a given (ergo…)
**Theory**: This is how it works, based on this **theorems** (It is…)
**Paradox**: A statement that can be shown, using a given set of **axioms** and definitions, to be both true and false (WTF!)
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**Grand Unified Theory of Everything**: The ÜBER THEORY. (Oh my God… it is full of stars. Look…a Higgs Boson!)