- #1
kathrynag
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Homework Statement
If I have a group defined on the integers, by a*b=ab, how do I know if an inverse exists?
Also, define * on the integers by a*b=max{a,b}
Homework Equations
The Attempt at a Solution
I got 1/a as an inverse, but I'm thinking it's not a group since we don't know if 1/a is an element of the integers.
The max is confusing me.
I know I need to check associativity, identity, and inverse for a group.
a*(b*c)=a*max{b,c)
=max{a,max{b,c}}
(a*b)*c=max{a,b}*c
=max{max{a,b},c}
I'm already confused at this point.