Because unlike 0.99..., 0.00...1 is not a Real number. The decimal representation of a Real number has to be indexed by Natural numbers, i.e. every decimal dig

Because unlike 0.99..., 0.00...1 is not a Real number. The decimal representation of a Real number has to be indexed by Natural numbers, i.e. every decimal digit[n] has a well-defined index n which is a Natural number. Infinity is not a Natural number, so 0.00...1 is not a Real number either.