Nitpick: non-random numbers are rare (this word is usually formalized as "the set of all non-random numbers has measure zero"), but still uncountable. The set of computable sequences is countable, but it is only a tiny subset of non-random sequences. For example, 0.0x₁0x₂… is non-random (= partially predictable) for any sequence x₁x₂…, and this set is obviously non-countable.