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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!)