Rhyming Forms A Monoid

The definition of a monoid:

I understand pulling this from a video is silly.

Anyway,

1. A set of elements

Consider w ∊ English words. (s∊Syllabels)? ## 2.Binary operation: Consider the function ℜ(w)->w EX: ℜ(dog)->log

What’s interesting to me here is that the heuristic for how w is obtained doesn’t matter. all that matters or all that we need to know is that ℜ of w returns w. ## 3. The operation is associative:

graph LR
                dog("A: dog") -->|F| log("B: log")
                log -->|G| cog("C: cog")
                dog -->|H| cog

4. The set contains the neutral element.

In this case the neutral element can be many words depending on the context. Bit like music in that way as in when you’re descending things are different versus when you’re ascending even if you’re using the same notes. Consider this example:

Definition of a perfect rhyme: A rhyme in which every syllable in word a rhymes with every syllable in word b.

Assume that all words that perfectly rhyme are the neutral element. IE:

ℜ(a)->b ℜ(dog)->log

It’s almost a bit like congruency. Like I should see how to form a category out of that and maybe it could help me. But for right now it feels right that two perfect rhymes should give another perfect rhyme which is a neutral element.

5. The set is closed under the operation

By definition the rhyming function ℜ(w)->w is closed under the operation.