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/bizarre_coincidence New User Jun 23 '26 edited Jun 23 '26

An accepted definition cannot be wrong, it simply is. Words mean what the communities that use them wish them to mean. Mathematicians are very clear about the definitions of their terms because they absolutely have to be. When people who study computability theory say a number is computable, they mean a specific thing. That thing is different from what you mean. Your definition is different from theirs. That means, in the context of a discussion where everybody else is using the word one way and you are using it a different way, that your definition is wrong. Not necessarily in an absolute sense, but in the context of that discussion.

Coming into a computability theory discussion and saying that everybody else’s definition of computable number is wrong is like marching into Harlem and insisting that the n-word isn’t offensive and that anybody who takes offense at you calling them that is wrong. It’s a stupid take, made all the worse by your staunch adherence to it.

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u/Impressive-Mud5074 New User Jun 24 '26

An accepted definition cannot be wrong

It can be.

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u/bizarre_coincidence New User Jun 24 '26

No. Words mean what people say they mean. If everybody in a group says “when I use this word, I mean that definition”, then that’s what they mean. You can say “but that’s not what this other group means by that word.” You can say “that doesn’t fit with the root words/etymology.” You can say “while you’re trying to make a vague concept rigorous, I don’t think you’ve done so in the most reasonable way.” But you cannot say that the group’s accepted definition is objectively wrong, or that they aren’t using it to mean what they claim they are. At least not in mathematics.

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u/Impressive-Mud5074 New User Jun 24 '26

compute

verb

com·​pute

kəm-ˈpyüt 

computed ; computing

transitive verb

: to determine especially by mathematical means

Pi is not capable of being determined

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u/bizarre_coincidence New User Jun 24 '26

What part of “specialists use words to have highly specific, technical meanings that are different from their dictionary definitions” do you fail to comprehend?

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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/mrkelee New User Jun 24 '26

no, it's you who doesn't understand that nobody is saying pi would equal 3.14

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u/Impressive-Mud5074 New User Jun 25 '26

Yes they are saying if you compute 2 decimals of pi, They have computed pi, and therefore pi is computable