It is known that "the integers under addition" form a group,(adsbygoogle = window.adsbygoogle || []).push({});

that is (Z,+).

I have always wondered how to actually proof that (Z,+) is a group?

Definitions for a group from wikipedia:

http://en.wikipedia.org/wiki/Group_(mathematics)#Basic_definitions

I'm especially interested in two things:

1) Why does the associative law hold for (Z,+), that is

a+(b+c) = (a+b)+c for a,b,c in Z.

And moreover:

2) Why is closure fulfilled?

That is, if a and b in Z, then a+b is also in Z.

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# Group axioms - Verify?

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