Question

I think postulates and axioms are quite similar, but how are they different?

Answer 1

Scientific types postulate, math types axiomize (is that a word?)

Answer 2

axiomatize

Answer 3

axiomatific! thanks.

Answer 4

axiom is a self evident truth right.. postulate is a forming opinion

Answer 5

axiom might or might not be self evident truth.

For instance the axiom of infinity and the axiom of choice are not obviously true.

Then again, the truth is not the issue, consistency is.

Answer 6

When Euclid started with his basic definitions, he assumed certain properties, which were "obviously universal truths. They were taken to be true because not even one example disproving them could be cited. He divided them into two types - axioms and postulates.

He used the term "postulate" for assumptions that were specific to geometry.
e.g. 1) A straight line may be drawn from any one point to any other point.
e.g. 2) all right angles are equal to one another.

"Axiom", on the other hand was used for assumptions that could be used throughout mathematics and not specifically linked to geometry.
e.g.1 ) Things which are equal to the same thing are equal to one another
=> This can be used for line segments, angles etc. in geometry.
=> also, 3+5 = 8 and 2+6 = 8 means 3+5 = 2+6
e.g. 2) If equals are subtracted from equals, the remainders are equal.
=> This also we use in geometry when we subtract equal angles or lengths from given equal angles or lengths.
=> also, 4+ 9 - 3 = 6 + 7 - 3

Answer 7

@Harkirat

True.

Maybe i will alter my answer a little bit and say that postulate relates to "real world" (ie applications) and axioms not necessarily so.

Answer 8

thanks estudier....

Actually these terms were coined long back and have been carried forward. Over a long period of time various additional meanings have cropped up, but this is how Euclid described them when he coined them.....

Answer 9

thank you! now i get it:)