Mathematics Poetry

roup: n. collection, cluster, set, assembly

“Define a group,” the student asks.

(I hope I’m equal to the task

of showing that by “group” is meant

more than a set of elements.)

We’ll need a set that’s well-defined,

where pairs of elements combined

are members of the set as well.

(He’s with me, so far, I can tell!)

The rule for forming combinations

Must hold for all associations,

Although commutativity

Is not a real necessity.

Except for the identity.

(But that’s a special case you see!)

Indeed, this member of the set

Is that peculiar element,

Which paired with any other there

Returns the other of the pair.

What’s more each member of the set

Must have a partner element,

Which pair combined must always be

This very same identity!

The student looks a little dazed.

Now, is he lost or just amazed?