“Standards of clothing” is not a set with a total order, and society has never had one way to dress. You’re unfairly projecting your values (of a certain style of dress) onto society as if it’s shared by everyone.
This is not maths, and nothing is shared by everyone in a human society.
I am actually an algebra major and I always felt that the need of some of my peers to stuff the entire outside world into mathematical definitions does not lead anywhere. Please don't mathematize societal concepts ("a set with a total order"), you will only mislead yourself and others. Maths isn't a good tool to understand people.
Let us talk about humans in a human language instead.
