@brainandforce @cll7793 A really simple one that fits here: The interval (0,1) and all the real numbers (-inf,+inf) have the same cardinality. The arctan function for example can be used to get a bijection.

Another simple consequence of Cantor: There are real numbers and integer sequences which we cannot ever compute or even hope to describe with words! Turing machines and possible strings of words are countable, real numbers are not countable.