>>11892853Look here, fat. Let N be the natural numbers, N={1,2,3,...}. N is unbounded, yes? Now take x to be any object that is not a natural number. Form a new set N' = N union {x}. Now we form a new ordering by declaring a<'b if and only if a,b are both natural numbers and a<b or b=x and a!=b.
With this new ordering <', we've extended the ordering < to a larger set and now the pair (N' , <' ) is bounded.
It's the same exact thing with the reals.
