It is a famous anecdote that Cantor was not quite as surprised when he came up with his "diagonal proof" (reals are uncountable) but when he saw that the points

It is a famous anecdote that Cantor was not quite as surprised when he came up with his "diagonal proof" (reals are uncountable) but when he saw that the points on the plane can be mapped to points on the line, i.e. the infinities are the same. There just seems to be more points in R^2 than R, this is highly counterintuitive.