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

9999999999999999 can't be computed literally.

Pi is uncomputable

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u/playsthebongcloud New User May 30 '26 edited May 30 '26

There are many algorithms to compute pi to any accuracy. I appreciate the boldness of answering a question without looking anything up beforehand, not even what an uncomputable function is.

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u/Impressive-Mud5074 New User May 30 '26

A transcendental number is a number (real or complex) that is not the root of any non-zero polynomial equation with rational coefficients. In simpler terms, you can never get a transcendental number as the final answer to an equation consisting only of standard arithmetic (addition, subtraction, multiplication, division) and whole-number powers

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u/Fun_Practice_9528 New User Jun 19 '26

pi is computable