Differences
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group [2014/12/18 18:48] nikolaj |
group [2015/02/02 19:02] nikolaj |
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| | @#55EE55: postulate | @#55EE55: $\forall g.\,\exists g^{-1}.\;(g*g^{-1}=g^{-1}*g=e)$ | | | @#55EE55: postulate | @#55EE55: $\forall g.\,\exists g^{-1}.\;(g*g^{-1}=g^{-1}*g=e)$ | | ||
| + | ----- | ||
| === Alternative definitions === | === Alternative definitions === | ||
| Let $\langle G,* \rangle $ be a set $G$ with a binary operation. I'll rewrite the group axioms explicitly in the first order language: | Let $\langle G,* \rangle $ be a set $G$ with a binary operation. I'll rewrite the group axioms explicitly in the first order language: | ||
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| ----- | ----- | ||
| - | |||
| === Subset of === | === Subset of === | ||
| [[Monoid]], [[Loop]] | [[Monoid]], [[Loop]] | ||
