I need to show that (0,1) and (10, infinity) have the same cardinality. Can I use similar triangles with open intervals? For example, I defined the open interval (10, infinity) to be on the positive x-axis and (0,1) to be on the positive y-axis. Then I said to pick any point in the interval on the x-axis that is greater than 10 and call it x. the corresponding point on the y-axis is f(x). By extending the line from x to f(x) out to point P @ (-1,1) we get two triangles. So f(x)/1 = (x - 10)/ (x + 1) where x > 10 is a function showing the bijection.
sounds reasonable.
Or, you can pair up values in (0,1) with values of f(x) = 10/x