- #1

kathrynag

- 598

- 0

## 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.