/sci/ - Science & Math

>>4859620
If it would be a quiz, I'd answer a sufficient condition is for B to be the trivial group, harhar.

No idea for a real answer though, OP.
What are your ideas so far?

Question /sci/

With the operations

<span class="math">x\ \rightarrow \ x+1[/spoiler]

as well as

<span class="math">x\ \rightarrow \ -\frac{1}{x}[/spoiler]

and starting from any integer, what subset of the reals can you generate?

Clearly you get all integers n, then <span class="math">\frac{1}{2}[/spoiler], because you get that from -2 with the second relation, i.e. you have all numbers <span class="math">n+\frac{1}{2}[/spoiler] with an n integer. Then if you apply the other rule you get <span class="math">m\frac{1}{n}[/spoiler], where m and n are some integers, then 1/(m+1/n), then 1/(m+1/n)+k ans so on.
My question is which numbers you can generate this way - which subset of the reals? Maybe all rationals? If not, which numbers are they?