Cantor carried the concept of the ‘countable infinity’, which he termed א0 (Aleph – nought) to the ‘indenumerable infinity’ which he named א1 (Aleph-one). [A very readable account of Cantor’s work is given in ‘Fractals – Images of Chaos’ ]. Note here that the description ‘countable infinity’ also means ‘that which in principle can be counted’ and it can also be termed as ‘denumerable infinity’.The ‘indenumerable infinity’, א1 is likened to ‘that which cannot be counted’ and is part of the continuum. Cantor developed ‘degrees of infinities’ between א0 to א1 by using one-to-one correspondence between the elements of two sets.
We see the one-to-one correspondence between the two sets and we conclude that since every number has its match – both the sets approach the same degree of infinity – in this case א0.