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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.
is it corret
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.
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then wt is associative axiome?
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 \(S\).
Just curious, but is this for group theory?
this is used in which field ?
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?