304 views

Let $\text{S}$ be the set of rational numbers with the following properties:

1. $\frac{1}{2}\in \text{S}$
2. If $x\in \text{S}$ then both $\frac{1}{x+1}\in \text{S}$ and $\frac{x}{x+1}\in \text{S}$

Which of the following is true?

1. $\text{S}$ contains all rational numbers in the interval $0 < x < 1$.
2. $\text{S}$ contains all rational numbers in the interval $-1 < x < 1$.
3. $\text{S}$ contains all rational numbers in the interval $-1 < x < 0$.
4. $\text{S}$ contains all rational numbers in the interval $1 < x <\infty$.

1 vote
1
289 views
1 vote
2
488 views
1 vote