Perhaps this is a strange question. But it made me think and I have no idea how to answer it. Or if it actually makes sense.
I've come across "Well-Ordered Sets" a few times now, and it's well known that there are different (nonisomorphic) ways of Well-Ordering Infinite Sets of any cardinality. On the other hand, there is only one (up to isomorphism...) way to well-order a finite set of size n. Also well known.
Furthermore, there is only one way to totally order a finite set of size n. Obviously this is not true for infinite sets either, as totally ordered sets are simpler than well-ordered sets (and so they are a superset of them).
The thought occurred to me, is there some kind of rigorous theorem, whereby the second statement, that there is only one way to totally order a finite set of size n, is the "simplest" of it's kind?
It seems hard to make the statement any simpler, as we did when moving from well-orders to total orders. Does/can this make rigorous sense?
Any help/quibbles appreciated!