rationalskepticism.org

This is intended as proof that the set of irrationals is larger than the set of integers, as well as that the set of irrationals is not countable.

But we cannot possibly "count" irrationals in order, like we do integers. Notice that there is no way you could ever make a chart like this in the first place, since you could never choose a first irrational after zero. That first irrational in the chart has an infinite number of a's in it. And, whichever "first irrational" you choose, I can choose a smaller one.