Is this true, that if we can describe any (real) number somehow, then it is computable?
For example, $\pi$ 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 $\pi$. If it wasn't than we were unable to calculate $\pi$ 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?