[Math] Why does the sequence ${1/n}$ not converge in the positive reals

Question

I'm reading Baby Rudin at the moment and it claims something remarkable. Consider the sequence

$$ x_n=\frac{1}{n}.$$

The book claims that this converges to zero in the reals:

$$\lim_{n\to\infty} x_n=0.$$

It also claims that it does not converge like this in the positive reals. Why is this?

Answer 1

Because $0$ is not a positive real!