I read that the power of $(0,1)$ is $2^\mathbb{N_0}$ due to the fact that $(0,1)$ is equipotent, roughly speaking, to the set of all binary representations of the numbers in $(0,1)$ (and this set has itself a power of $2^\mathbb{N_0}$).
But $(0,1)$ can be also put in bijection with, say, all the base-10 number representations. Wouldn't that render a power of $10^\mathbb{N_0}$ for $(0,1)$?
Thank you in advance.
Andy.