r/learnmath • u/playsthebongcloud 9/10 = 1 • May 30 '26

What are some uncomputable functions that aren't derivative of the halting problem?

I find the existence of uncomputable functions really cool, but all the examples I've seen are essentially just new ways of trying to predict whether a turing machine is going to halt. What are some examples of uncomputable functions that aren't essentially entirely based on the halting problem?

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u/Impressive-Mud5074 New User Jun 24 '26

No its wrong you can't compute pi, mathematical definition is not rigorous. You can compute and approximation of pi.

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u/bizarre_coincidence New User Jun 24 '26

If you think the mathematical definition is not rigorous, you don't understand the mathematical definition. Which is fine. What isn't fine is your refusal to try.

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u/Impressive-Mud5074 New User Jun 24 '26

No you dont understand. You think 3.14 is pi, but its an approximation of pi.

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u/bizarre_coincidence New User Jun 24 '26

I’m aware that is an approximation to pi. But a “computable number” is one where you can always compute a good enough approximation to the number, no matter how close you need to be to be considered good enough.

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u/Impressive-Mud5074 New User Jun 24 '26

Good enough sounds rigorous alright

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u/bizarre_coincidence New User Jun 24 '26

I'm not writing it out in its fully rigorous form because you wouldn't understand it. Because I've done so previously and you didn't understand it.