Question

what is the key point of differentiating a theorem, definition and postulate?

Answer 1

I have come across these three types many times. But I can't understand the difference between them. So I am looking for a simple statement of identifying the difference between them.

Answer 2

I think this might help, although it's probably not the most precise thing in the world.

A postulate is something that's assumed to be true, synonymous with being an axiom. In other words, you can't prove it but you can use it to prove other things, kind of like a starting point.

A definition is more like something you describe, like you can define a triangle to be 3 points connected by 3 lines in space. It's not really something you need to prove, it's just giving something a name.

A theorem is something you prove based on your postulates and you can use your definitions to help simplify how you talk about it.

Answer 3

a definition introduces the most fundamental objects to a system.

a postulate introduces the most fundamental unquestionable relations between those objects.

a theorem introduces more relations that are proven using postulates, i.e., those unquestionable relations.

Answer 4

@Kainui yes. wikipedia also describes what you said.

Answer 5

okay. I understand that a theorem is something you should be able to prove. But definition and postulate seems to be same.