# Are there any examples of non-computable real numbers?

Is this true, that if we can describe any (real) number somehow, then it is computable?

For example, $$π\pi$$ is computable although it is irrational, i.e. endless decimal fraction. It was just a luck, that there are some simple periodic formulas to calcualte $$π\pi$$. If it wasn’t than we were unable to calculate $$π\pi$$ ans it was non-computable.

If so, that we can’t provide any examples of non-computable numbers? Is that right?

The only thing that we can say is that these numbers are exist in many, but we can’t point to any of them. Right?

I haven’t thought this through, but it seems to me that if you let $BB$ be the Busy Beaver function, then should be a noncomputable real number, since if you were able to compute it with sufficient precision you would be able to solve the halting problem.