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 $b$?
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user21820, user26857, JMP, Rohan, user91500
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.)
Of course, it is true. The set of all algebraic numbers is countable, while the whole interval is uncountable.