so there is this thing define as the set of all numbers in the form of $$V=\{\exp(k_0\cdot \exp(k_1\cdot \exp(\ldots k_{n-1}\cdot \exp(k_n)) \mid k_i=\pm1\} $$
I asked my teacher that if I let $n$ approach infinity, would $V$ span the positive reals. He said that it would probably just be dense over the reals, but he is not sure. How would I go about proving it?