Really mathy definitions

Sure, let’s define these concepts mathematically using sets and functions.

Set of Perfect Rhymes

Let ( S ) be the set of all possible syllables in the English language. Let ( W ) be the set of all words in the English language. Define a function ( : W S^* ) that maps each word to its sequence of syllables.

Define the set of perfect rhymes, ( R ), as follows:

[ R = { (w_1, w_2) W W (w_1) = (w_2) w_1 w_2 } ]

Identical Rhymes

Define the set of identical rhymes, ( I ), as follows:

[ I = { (w_1, w_2) W W (w_1) = (w_2) w_1 w_2 } ]

Summary

• Perfect rhymes: Words that have the same syllables but differ only in their beginning consonants.
• Identical rhymes: Words that have the same exact syllables but are different words.

Mathematically: - Perfect rhymes: [ R = { (w_1, w_2) W W (w_1) = (w_2) w_1 w_2 } ] - Identical rhymes: [ I = { (w_1, w_2) W W (w_1) = (w_2) w_1 w_2 } ]

Mathematically, a homophone can be defined using sets and functions as follows:

Let ( P ) be the set of all phonetic transcriptions (phonemes) in a language, and ( W ) be the set of all written words (orthographic representations) in that language. Define a function ( : W P ) that maps each word to its phonetic transcription.

Two words ( w_1, w_2 W ) are homophones if and only if:

[ (w_1) = (w_2) w_1 w_2 ]

This means that ( w_1 ) and ( w_2 ) have the same phonetic representation but are different words.

The levenshtein distance over the set of perfect rhymes under syllables m is 1,

Which can also form a pre order where everything is less than equal to itself.