What is a Theorem, Corollary, Conjecture, Lemma, Axiom, and Proposition?

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In this video, I will explain the differences between a theorem, corollary, conjecture, lemma, axiom, and proposition. You need to know these terminologies if you are taking a class about proofs or discrete mathematics. A proposition is a statement that is either true or false. An axiom is a statement that we assume to be true (self-evidently true) and we do not need to prove it. A lemma is a small result that has been proved, and it is used to prove a theorem. A theorem is a significant result that has been proved. A corollary is a theorem that follows on from another theorem. A conjecture is something that someone (usually a famous person) says is true but they have not been able to prove or disprove it.
  1. Quoc Dat Phung
  2. theorem
  3. corollary
  4. conjecture
  5. lemma
  6. axiom
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Straight to the point and informative, very helpful video!

spaceiscool
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What about “ 2+ 2 = 4” is this an axiom because we cannot prove it is true but we assume it is?

MathCuriousity
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Also out of curiosity can you help me understand what an “axiomatic approach” in math is and what would the opposite approach be?! I thought ALL math fields were axiomatic?

MathCuriousity
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Wait a minute. I just read that a proposition is statement that has been proven true - just like a theorem - except not as important.

MathCuriousity