Can You Compute This?

Probability Level 4

A computable number is one which, given enough time, can be calculated to whatever degree of precision is desired. For example, the irrational number which has a 1 in every prime slot 0.01101010001010001 0.01101010001010001 \ldots is computable. To calculate it to an accuracy of 10n 10^{-n} , we just need to determine which of the first nn positive integers are prime.

Are there countably many or uncountably many computable numbers?

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