Take this mathematical structure for example:
(Z, #) where Z is the set of all integers and where a#b returns the larger of the two elements.
In order to prove this is a group I must prove these four properties: -Closure -Associative -Identity -Inverse
I am stuck on the Identity Element. As far as I know, the only element e that would prove to be true so that a#e = a = e#a would be -infinity. Is this possible, or would this mathematical structure just fail to be a group?