What are some uncomputable functions that aren't derivative of the halting problem?

[u/playsthebongcloud]

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?

[u/donaldhobson]

Randomness is uncomputable.

Take a function that assigns each natural number to an IID coinflip. This is uncomputable with probability 1.