- #1
smurf_too
- 11
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Let G be a finite nonempty set with an operation * such that:
1. G is closed under *.
2. * is associative.
3. Given with a*b=a*c, then b=c
4. Given with b*a=c*a, then b=c
Give an example to show that under the conditions above, G is no longer a group if G is an infinite set?
1. G is closed under *.
2. * is associative.
3. Given with a*b=a*c, then b=c
4. Given with b*a=c*a, then b=c
Give an example to show that under the conditions above, G is no longer a group if G is an infinite set?