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group [2015/02/02 19:02] nikolaj |
group [2015/04/16 19:17] (current) nikolaj |
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| === 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: | + | == Sharper definitions == |
| + | We could just define left units and left inverses and prove from the group axioms that they are already units and inverses. | ||
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| + | == Group axioms explicitly in the first order language == | ||
| + | Let $\langle G,* \rangle $ be a set $G$ with a binary operation. | ||
| 1. $\forall (a,b\in G).\ (a*b\in G)$ | 1. $\forall (a,b\in G).\ (a*b\in G)$ | ||
