Question

what is closure axiom?

Answer 1

I guess that depends on what you're working with. Generally though, it would be something like:

Given a function \(f:S\times S\to T\), where \(S,T\) are sets, then \(T\subseteq S\).

This probably isn't the wording you need, but that's the general idea of closure.

Answer 2

is it corret

Answer 3

I'm honestly not sure exactly how correct this is. I just kind of made that up based on what I knew closure was. I am sure that it captures the general idea though.

Answer 4

then wt is associative axiome?

Answer 5

Doing a little research, it seems that it's called the axiom of closure if the function can take any element of \(S\) as an input, and outputs another element of \(S\).

Answer 6

Just curious, but is this for group theory?

Answer 7

this is used in which field ?

Answer 8

Anyways, if \(f:S\times S\to S\) is your function, then the associative axiom is that \(f(f(a,b),c)=f(a,f(b,c))\). If you're working in a group or field or similar, you usually write that \(a\cdot(b\cdot c)=(a\cdot b)\cdot c\) for \(a,b,c\in S\).

Does this make sense?