# Tagged Questions

For questions about decimal expansion, both practical and theoretical.

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### Variation of the Kempner series – convergence of series $\sum\frac{1}{n}$ where $9$ is not a digit of $1/n$.

It is easy to argue that the Kempner series converges: $$\sum\limits_{\substack{n \text{ s.t. 9 is}\\\text{ not a digit} \\\text{ of } n}} \frac{1}{n} < \infty$$ Let $E \subset \Bbb N_{>0}$ ...
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### Error with the proof that all solutions to the Cauchy Functional Equation are linear

If $f(x)$ is continuous, it is known that $f(x+y)=f(x)+f(y)$ implies that $f(x)$ is linear, and non-continuous solutions are discussed in these links. (1, 2,3, 4) However, what is wrong with this ...
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### What points in $[0,1)$ will have two binary expansions?

What points in $[0,1)$ will have two binary expansions? I know that $\frac{1}{2}$ has the two expansions $0.1\bar{0}$ and $0.0\bar{1}$ $0.1\bar{0}$ is found by starting with $\frac{1}{2}$ and ...
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### Measurability of set of numbers with infinite number of digits in decimal expansion equal to 8

Say A is the set of all Real numbers on $[0,1]$ whose decimal expansion contains an infinite number of 8s. I am trying to prove the measurability of this set. I realize that this is the set of ...
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### 3-digit chopping vs 3-digit rounding and relative error

3-digit chopping, 3-digit rounding, relative error: Would my calcs below be correct: given 4/5 * 1/3: Exact value: 0.2666666666666667 3-digit chopping: 0.266, its relative error: 0.0025 ...
### Is the last digit of this number :${{4^4}^n}+1$ always $7$ for $n>1$ and could this be prime?
Some computations in wolfram alpha for $n=2,3,4,5 ,6$ showed that the last digit of this number ${{4^4}^n}+1$ for $n>1$ always $7$ . My question here :How do I know if it's last digit always ...