There is a difference between countably and uncountably infinite. Countably infinite is when you have a one-to-one correspondance with the natural numbers. Un

There is a difference between countably and uncountably infinite. Countably infinite is when you have a one-to-one correspondance with the natural numbers. Uncountably infinite is when you have even more. Note that one can come up with a proof that the number of equivalence classes should be uncountably infinite using the method of the Candor diagonalization argument.