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If $a$ and $b$ are real numbers and $a<b$ is it true that there is an uncountable number of transcendental numbers between $a$ and $b$?

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closed as off-topic by user21820, user26857, JMP, Rohan, user91500 Feb 15 '17 at 11:04

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Yes, there are.

Any (nonempty) interval $(a, b)$ is uncountable, and the union of two countable sets is countable. So all you need now is the fact that the set of algebraic numbers is countable. HINT: how many polynomials with rational coefficients are there? (If you want more details see this question.)

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Of course, it is true. The set of all algebraic numbers is countable, while the whole interval is uncountable.

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