DIFFERENCE BETWEEN AXIOM, POSTULATE AND THEOREM

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Axiom
  • Oxford dictionary definition: A statement or preposition which is regarded as being established, accepted, or self-evidently true.
  • Cambridge dictionary definition: A statement or principle that is generally accepted to be true, but need not be so.
  • Example: Peano axiom- For every natural number n, S(n) is a natural number.


Postulate
  • Oxford dictionary definition: A thing suggested or assumed as true as the basis for reasoning, discussion, or belief.
  • Cambridge dictionary definition: To suggest a theory, idea etc. as a basic principle from which a further idea is formed or developed.
  • Example: Euclid's postulate- A straight line segment can be drawn joining any two points.


Theorem
  • Cambridge dictionary definition: A formal statement that can be shown to be true by logic.
  • Oxford dictionary definition: A general preposition not self-evident but proved by a chain of reasoning; truth established by means of accepted truths.
  • Examples: Pythagoras theorem, Fundamental theorem of arithmetic etc.

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