> From: Dave Seaman <dsea...@no.such.host> > The fact that the real numbers are everywhere dense (meaning > between any two reals, there are others) is precisely the fact > that prevents gaps from existing.
It makes a difference whether you're talking about gaps between any two individual numbers, and gaps between two *sets* of numbers. Lack of gap between two indivual numbers = dense Lack of gap between two sets of numbers = complete
Rationals are dense but not complete. Reals are both dense and complete.