Abstract Algebra/Group Theory/Group/Cancellation
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- Let G be a Group.
0. Choose such that 1. definition of inverse of g in G (usage 1) 2. 0. 3. is associative in G 4. g-1 is inverse of g (usage 3) 5. eG is identity of G(usage 3)
- if a, b, x are in the same group, and x*a = x*b, then a = b
- a, b, and g have to be all in the same group.
- has to be the binary operator of the group.
- G has to be a group.