I'm perplexed by the question. The CH is: there is no cardinality between that of the set of integers and set of real numbers. (My argument:) But clearly the set of integers takes up a smaller region under a curve than does the rational numbers and the same for rational numbers compared to real numbers. Cantor himself proved that the integers are a smaller set than that of the real numbers. So is the CH true or false or maybe even somewhat, bogus?