>Each time you reduce a number via square root you will eventually reach an infinite response and thus it's impossible to solve, let alone with a binary compute

>Each time you reduce a number via square root you will eventually reach an infinite response and thus it's impossible to solve, let alone with a binary computer system. This is incorrect. All the symbolic math programs in the world provide counterexamples. There is no need to deal with infinite length decimal numbers to do a lot of proving of things in mathematics, in the same manner when I prove things by hand I do not need to write out infinite length numbers. Your mistake is assuming the only way to analyze a sqrt of a number is to write it out in infinite precision. That is not needed. For example, you can prove on a computer that sqrt(19) > sqrt(17) without having to evaluate either side as a decimal number. For example, Mathematica (or any symbolic program), entering Sqrt[19]>Sqrt[17] returns True.