Constructive vs computable real numbers https://ift.tt/eA8V8J

I find it confusing that all of the following statements are true :

1. The computable real numbers are countable. $-\hspace{-3pt}-$ Alan Turing, "On Computable Numbers, with an Application to the Entscheidungsproblem"
2. In constructive analysis, the real numbers are uncountable. $-\hspace{-3pt}-$ Everett Bishop, Foundations of Constructive Analysis
3. "every mathematical statement [in constructive analysis] ultimately expresses the fact that if we perform certain computations within the set of positive integers, we shall get certain results" $-\hspace{-3pt}-$ Ibid.

Perhaps I am misunderstanding something.

I suppose I really have two questions. In constructive analysis :

1. Why isn't every real number computable?
2. How is it possible to construct an uncountable set?

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simple jack