> ∃ i ∈ S: ∀ x ∈ S, i # x = x # i = x.
> ∀ x ∈ S, ∃ y ∈ S: x # y = y # x = i.

Not that I wish to imply, in any way, that I'm bored or that my 
intellectual capabilities are not being fully utilised by my day job OR 
ANYTHING LIKE THAT... >_>

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