To show that the set of all real numbers between 0 and 1 had a higher cardinality than n_0, we assumed first that they had the *same* cardinality. then we showed that there was at least one number which was not counted in the list. suppose now that we *only* consider those numbers between 0 and 1 which have a decimal expansion consisting of 0’s and 1’s. (e. g. 0.10101…, 0. etc.) show that this set *also* has a cardinality greater than n_0 (once again by the same kind of construction).