Because it's numbers, which are sortable, you can ask which is the least member of a set. If a set of positive numbers doesn't have a least member, does the set

Because it's numbers, which are sortable, you can ask which is the least member of a set. If a set of positive numbers doesn't have a least member, does the set exist? There's a similar paradox which asks what the smallest number that can't be defined in fewer than thirteen words. There must be some number, right? For instance, 7603201560, or "seven billion six hundred and three million two hundred and one thousand five hundred and sixty" seems to require 16 words. Maybe you can shorten it by removing the "ands," but I can come up with a longer number. But if there were such a number, then couldn't we describe it as "the smallest number that can't be defined in fewer than thirteen words?" And then it just got defined in fewer than thirteen words. So it can't really be a member of that set. So does the set have any members?