- #1
jessicaw
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"How to prove that a set is a group?" related difficult/challenge quesyion.
1.In proving that a set is a group from definition, we have to show there is an inverse element for each element, do we have to show uniqueness of it?
I believe this is unnecessary but people do this all the time.
My argument:
"For each [itex]a\in G[/itex], there exists a left inverse a' in G such that a'a=e." is enough.
1.In proving that a set is a group from definition, we have to show there is an inverse element for each element, do we have to show uniqueness of it?
I believe this is unnecessary but people do this all the time.
My argument:
"For each [itex]a\in G[/itex], there exists a left inverse a' in G such that a'a=e." is enough.