Of course, for this to make any sense at all, we would need to know what axiom system this is describing a possible model of -- and whether it's a first-order or second-order theory. --Dan << . . . if the positive integers are closed under + and *, then if 1 is not the smallest positive integer there are infinitely many between 0 and 1. I'd be hard pressed to still call them "integers", but I guess that might be your nonstandard model -- say, all fractions whose denominators are powers of 2 or something like that?

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_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele