The catch

• How the heck do you do arithmetic on continued fractions?

  • How do you add, subtract, multiply and divide them?

• Or consider this:

        0    = [0]
        1/8  = [0; 8]
        2/8  = [0; 4]
        3/8  = [0; 2, 1, 2]
        4/8  = [0; 2]
        5/8  = [0; 1, 1, 1, 2]
        6/8  = [0; 1, 3]
        7/8  = [0; 1, 7]
        1    = [1]

• It seems that the only way to evaluate this is to turn both addends into rational numbers

• Which defeats the whole purpose

• And anyway doesn't work for infinite continued fractions