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Please provide the definition of "a postulate".
it can...but people prefer not to....mathematicians love to do it though....they are somewhat masochistic.....
Here's a definition I found. Definition of Postulate Postulate is a true statement, which does not require to be proved. A little odd with the grammar, but it does answer your question.
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. @tkhunny http://dictionary.reference.com/browse/postulate
@tkhunny your statement says that " postulates does not require to be proved" but can they be proved, is my doubt ...
Modern mathematician usage has 'axiom' and 'postulate' be interchangeable, but their original meanings are quite different.
There is some variation, depending on which author you read. This is why I ask SheldonEinstein to provide a working definition for this discussion.
Axioms cannot be proven because they are "self-evident" or "obviously true" which strict mathematicians and logicians don't like because they don't like to assume that anything is true. They don't allow things like a-priori knowledge or empirical evidence to influence their strictly formal logical sequences.
A 'postulate' is something that one requests to be accepted as true without proof, so that the discussion can move along to prove something of greater consequence.
Postulates are often axioms, but they can also be previously proven theorems that have already been accepted, and are being used as bases for additional proofs.
Oh OK got it now!
So : either they CAN BE proven or CAN NOT BE?
heh mathematicians love proving imaginary things
i think it's a psychological problem......i don't know.....
Definitive and final answer? Maybe. It is possible that some postulates can be "Proven", however, this is absolutely not the point of a postulate. Postulates are to be assumed so that we can observe the implications of the assumption. It would be entirely inappropriate to attempt to DISPROVE a postulate.
As an example, let's say I want to prove the statement, "The base angles of an isosceles triangle are congruent." First, you have to accept the definition of what an isosceles triangle is as a postulate, and also accept the axioms of things being equal to themselves, and that of equals added to or subtracted from equals leaves their sums or differences equal, and so on. A previously proven theorem, such as certain triangles having corresponding congruent elements being congruent can be used as a postulate to further along the proof of the current statement - without having to go back and re-prove the prior theorem.
^Nice example sir, agreed.
Thanks a lot guys, I think my doubt is clear now, Thanks @CliffSedge @tkhunny @lgbasallote
@lgbasallote 's notion of 'psychological problem' raises a good point. It depends on what you mean by "prove." This gets into philosophy of epistemology, etc. which shouldn't be allowed to bog down the work of mathematics.
In mathematics / logic / etc. One can "prove" *anything* as long as the postulates are accepted and the logical train of argument stays consistent and valid.
If you want "prove" to mean that a proposition necessarily corresponds to objective reality, then you have to take into account sensory perception, fallibility, empirical bases of conjecture, reach of explanation, difficulty to vary an explanation, the process of experimental testing and peer criticism. . . .
Me, though? I'd rather just lay out the rules of the game ahead of time and just play by the rules. As long as everybody stays consistent and all the explanations still work, I'm cool with it.
Thanks for your reply sir, I got it now!