2 word length doesn't map monoids but elements of monoids

Can you give a good example of this in another instance?

The Wikipedia definition seems to imply that if you do not have natural numbers defined yet, they follow as the lengths of the finite strings.

In particular, given any Free Monoid, the unique word length function maps elements of that monoid into the natural numbers.

1

Can you give a good example of this in another instance?

The Wikipedia definition seems to imply that if you do not have natural numbers defined yet, they follow as the lengths of the finite strings.

In particular, given any Free Monoid, the unique word length function maps that monoid into the natural numbers.