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In wikipedia we see that the words “axiom” and “postulate” are synonyms:

“An axiom, or postulate, is a premise or starting point of reasoning”.

But in A Friendly Introduction to Numerical Analysis we read:

“The axioms and postulates of the appropriate discipline(s) -be they from the physical, natural, or social sciences- are then used to develop a set of assumptions and a set of equations, known as a mathematical model, which will be used for subsequent analysis”.

Wikipedia used the “or” but the auther used the “and”. What is the difference between axiom and postulate?

Dante
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    AFAIK they are synonyms in mathematical usage. Possibly they have some slightly different meaning in the jargon of some other science. I doubt that this is any issue, though. – Giuseppe Negro Jan 06 '14 at 21:08
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    In Euclid's Elements he actually first has 5 postulates (i.e. axioms) then 5 "common notions" which seem to be like axioms, because they are so "obvious". The common notions are more fundamental than his axioms but they also don't give you much to work with. – Squirtle Jan 06 '14 at 21:11

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It seems that axioms and postulates refer to the same thing. From Dictionary.com, definition 6 of postulate:

Mathematics, Logic. a proposition that requires no proof, being self-evident, or that is for a specific purpose assumed true, and that is used in the proof of other propositions; axiom.

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JRN
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