Same as the cardinality of all reals. In fact, the cardinality of the set of all reals between 0 and 1 is the same as the cardinality of the set of all reals. https://en.wikipedia.org/wiki/Cardinality_of_the_continuum#Sets_with_cardinality_of_the_continuum

Glad you made me look! I hadn’t thought about whether there were sets with cardinality greater than the cardinality of the continuum. https://en.wikipedia.org/wiki/Cardinality_of_the_continuum#Sets_with_greater_cardinality