Different interactions with a resource may expose contents that vary with time, data format, preferred language, requestor credentials, etc. Radix 10, I guess. I'd suggest allowing leading zeros, but they don't change the denotation. But note, people often do want to distinguish 10 from 10.0 as being different kinds of thing, so be careful, if you allow decimals, to let people keep integers and reals separate. Similarly for signs and negative numbers.
Naturals are natural for counting things.
Might be better to phrase this as every y in S is greater or equal. The way you have it, S could contain some non-integers and still have a minimum. Similarly for max. Well, this isnt wrong exactly, but its also not a very good definition since it is a nonterminating recusion. This is actually quite tricky.