Can a mathematical difference not also imply a disjunction? Is there a disjunction for every difference? E.g. 2-1=1 which implies a disjunction e.g. the sets 1 and 2 are disjunct. So can there not be any difference that not also implies a disjunction?

The claim that numbers are sets is controversial; if they are not sets, talk of them being ‘disjoint’ doesn't make sense.

If one does identify numbers with sets, the best-known way of doing so is von Neumann's, on which each number is the set of its predecessors, so that in particular $0=∅$, $1=\\{∅\\}$ and $2=\\{∅,\\{∅\\}\\}$. On this approach, 1 and 2 are not disjoint, in fact $1⊂2$. And in general $x⊂y$ whenever $x≤y$.