Are all infinities the same? - Colegiul National C. Negruzzi (Iași - Roumanie)

The work deals with the comparison of the cardinalities of infinite sets of numbers. It is proved that: (1) the sets of natural numbers, prime numbers, integers, and rational numbers have the same cardinality, and (2) all intervals of real numbers have the same cardinality as R, which is higher than that of the natural numbers. Most of the results are proved by showing the existence or non-existence of bijective functions.)