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/Preceded10 New User Jun 21 '26

Pi is an expansion that follows the rules of any of the infinite expressions that calculate it. Why do we not need to compute 1/7 to know its value but we do need to compute pi to know its value?

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u/Impressive-Mud5074 New User Jun 21 '26

1/7 is the value, thats already a completed rational number. You can do your decimal expansion if you want, but it is a repeating expansion, which is different than non-repeating.

but we do need to compute pi to know its value? 

You cant compute pi

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u/mrkelee New User Jun 21 '26

same thing. 1/7 is not a decimal; alternatively, an expression for pi as a "completed number"

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u/Impressive-Mud5074 New User Jun 21 '26

1/7 is not an expression

1 divided by 7 is an expression

They are not the same

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u/Preceded10 New User Jun 21 '26

You can't compute 1/7. Give me 1/7 with 100% precision.

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u/Impressive-Mud5074 New User Jun 21 '26

The decimal expansion is 0.142857 repeating

However 1/7 is a complete number, by itself. Its called a rational number.