Defining a group using axioms.
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Define * on Z by a * b = max{a,b}. Is Z a group?
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No, Z is not a group under this definition.
We can not find the identity of the group.
If 0 is the identity, then (-1)*0=(-1). But by the definition, ...
Solution Summary
Group status is determined using axioms. The details are well presented in the solution.
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