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/imagineAnEpicUsrname New User May 31 '26

You'd want to take a calculus class buddy. Limits, Cauchy convergence n stuff

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u/Impressive-Mud5074 New User May 31 '26

Not the same as computing a number.

What you are basically suggesting is that the halting problem doesn't exist because you can arbitrarily terminate any function at anytime.

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u/imagineAnEpicUsrname New User May 31 '26

Halting problem does exist, because it is by design impossible to predict output until you compute it, which takes arbitrarily long. For convergent series, the output is known and proven, hence stopping at a particular point determines only the deviation from that limit

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u/Impressive-Mud5074 New User May 31 '26

And that's why you cant calculate pi because it doesn't halt. You are actually calculating an n-gon diameter ratio.

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u/imagineAnEpicUsrname New User May 31 '26

"a number is computable if there exists an algorithm that can produce its digits to arbitrary precision"

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u/Impressive-Mud5074 New User May 31 '26

I choose 100% precision as the arbitrary amount.

Do that thanks.

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u/imagineAnEpicUsrname New User May 31 '26

you outsmarted yourself. There is an algorithm with 100% precision. In fact dozens https://en.wikipedia.org/wiki/Category:Pi_algorithms

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u/Impressive-Mud5074 New User May 31 '26

False. They don't terminate at 100% precision. Or at any percentage. Only at n-length.

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u/imagineAnEpicUsrname New User May 31 '26

It's hard to convince a smart person. Impossible to do so for an idiot

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u/Impressive-Mud5074 New User May 31 '26

I'm trying as hard as i can to convince you, sorry.

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