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This is not a computer science question. It's a math challenge. We simply rely on computers to do the math faster. I challenge any math person to solve this

This is not a computer science question. It's a math challenge. We simply rely on computers to do the math faster. I challenge any math person to solve this problem and/or provide a proof. Given that their equations will ultimately be so complex they will fail. For example, just say 1/3. Easy right? 0.333333334 Wrong. It's impossible for a human or a computer to say the answer. NOT a CS issue. We can't combine random and ultimately repeating numbers. 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. I would love the very first quantum computer to do 1/3. Just use up all the CPU and energy it has in a problem it can't solve. Forever in time. Look not at the computer as the failure scenario but math in general. At some point you stop and round. When that happens, an error is introduced when you extend the answer beyond the rounding point. At some point you will fine an infinite answer and/or answers. I can write you a computer program to write a single infinite answer. Combining two of them produces the same infinite process. Here is a better answer. Can we shift the base in a way that allows us to answer random questions like these?

nestorD 5y ago
Computing the value would be a problem but determining which is bigger is purely a CS question (just one that cannot be solved directly with our usual floating point tool: IEEE 754 arithmetic).
monktastic1 5y ago
You may have missed the point. Although fractions may have infinite representations, the question of which sum of fractions is larger is a much easier problem to solve: "On the other hand, comparing the sums of fractions is pretty easy, because division is nice and well behaved. So the question is how complicated square roots are."
ChrisLomont 5y ago
>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.

nestorD 5y ago

Computing the value would be a problem but determining which is bigger is purely a CS question (just one that cannot be solved directly with our usual floating point tool: IEEE 754 arithmetic).

monktastic1 5y ago

You may have missed the point. Although fractions may have infinite representations, the question of which sum of fractions is larger is a much easier problem to solve: "On the other hand, comparing the sums of fractions is pretty easy, because division is nice and well behaved. So the question is how complicated square roots are."

ChrisLomont 5y ago

>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.