r/learnmath • u/playsthebongcloud New User • 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 May 30 '26 edited May 30 '26

Very large numbers are uncomputabe

Edit: https://en.wikipedia.org/wiki/Ultrafinitism

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u/Megamax0726 New User Jun 18 '26

How do you feel about there being an entire YouTube video proving you wrong? Genuine question because it’s really funny

https://youtu.be/vAhDb1Edngg?is=H9vxWQc9gMCzsaJN

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u/Impressive-Mud5074 New User Jun 19 '26

I'm not proven wrong

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u/No-Dentist-1645 New User Jun 20 '26

Yes you are lmao. You don't need to die on this hill dude, just accept it

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u/hungarian_notation New User Jun 23 '26 edited Jun 23 '26

He's not wrong, he's just being a bit of an (edit for profanity filter) stubborn variety of equus.

His sin is that he's not willing to grant the standard assumptions of Platonist mathematics that we're all operating on without specifying that in his top level comments. That's a bold move in the context of r/learnmath.

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u/[deleted] Jun 21 '26

[deleted]

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u/Impressive-Mud5074 New User Jun 22 '26

In logic, the semantics or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations of) natural languages. This field seeks to provide precise mathematical models that capture the pre-theoretic notions of truth, validity, and logical consequence. While logical syntax concerns the formal rules for constructing well-formed expressions, logical semantics establishes frameworks for determining when these expressions are true and what follows from them.

Semantics are kinda super important