> But that set must have a member whose value is closest to zero. Must it? "Let x be the smallest element of the half-open interval (0, 1]" isn't really somet

> But that set must have a member whose value is closest to zero. Must it? "Let x be the smallest element of the half-open interval (0, 1]" isn't really something that you can say *. * Assuming the standard ordering of reals; sure you can say it's defined for some well-order, but then you require the Axiom of Choice anyway.