Word rhyming is an equivalence relation
Take the definition that two words rhyme if and only if they end with the same sound.
Reflexive: Every word rhymes with itself.
Well, if two words are the same, all their sounds have to match, including the final one, so this point holds.
Symmetric: If A rhymes with B, B rhymes with A.
This one’s really hard to prove, because it’s so obvious. If A rhymes with B, then the final sounds of A and B are the same. They will still be the same if we swap the words around. Please don’t make me explain it more, I’ll cry.
Transitive: If A rhymes with B and B rhymes with C, then A rhymes with C.
Call the sound at the end of word A ‘&’. If A rhymes with B, then B also has to end with ‘&’. If B rhymes with C, and B ends with ‘&’, then C also has to end with ‘&’. This means that both A and C end with ‘&’, and so A rhymes with C.
There we go. The argument no one cares about but me has been made. Rhyme is an equivalence relation. You can all go home.
