This re-instated what passes for faith in humanity

[--Pete]

Hi,

One can put the fractions in one-to-one correspondence with the natural numbers e.g. put all (positive -- which makes no difference)  fractions in a square:

1/1  2/1  3/1  4/1 ...
1/2  2/2  3/2  4/2 ...
1/3  2/3  3/3  4/3 ...
1/4  2/4  3/4  4/4 ...
....

and count them starting at the top left corner down diagonals, neglecting repeats (i.e. 1/1 2/1 1/2 1/3 (2/2) 3/1 4/1 3/2 2/3 1/4...)

So the set of fractions has the same cardinality as the set of integers, and smaller cardinality than the set of real numbers.
[right][snapback]98339[/snapback][/right]

You don't even need to neglect the repeats and it still works :)

--Pete