In practice constructible for reals mean that you can approximate them with arbitrarily small know precision e.g. a sequence of retional number numbers q_n eac

In practice constructible for reals mean that you can approximate them with arbitrarily small know precision e.g. a sequence of retional number numbers q_n each no more that 1/n apart from the actual real number. The point is that such a sequence needs to be constructive in the usual sense, so there are still only a countable number of them.