anonymous
  • anonymous
what is closure axiom?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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Armor
  • Armor
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.
anonymous
  • anonymous
is it corret
Armor
  • Armor
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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anonymous
  • anonymous
then wt is associative axiome?
Armor
  • Armor
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 \(S\).
Armor
  • Armor
Just curious, but is this for group theory?
anonymous
  • anonymous
this is used in which field ?
Armor
  • Armor
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?

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