Are you sure ? only "one" infinity?
We know "ℝ" is infinity.also "(1,0)" is infinity.
We can also say that we are able to place (1,0) on ℝ.so ℝ is more powerful than (1,0) so they are different.
I mean ℝ-(1,0) is also infinity.
Please think about what I said. Are'nt you agree?