1. Counting the fractional binary numbers

2. Fractional binary numbers on the real line

3. Countability of BF

4. Set of all binary numbers, B

5. On Cantor's diagonal argument

6. On Cantor's theorem

7. On infinite digital expansion of irrational number

8. On the continuum hypothesis

Please read the article at

Cardinality of the set of binary-expressed real numbers

PengKuan on Maths: Cardinality of the set of binary-expressed real numbers

or

https://www.academia.edu/19403597/Cardinality_of_the_set_of_binary-expressed_real_numbers