So this is pretty obvious in what it is asking: To prove that anything between $0$ and infinity are part of the positive reals.
I feel kind of stupid for asking but I just don't even know where to start. The topic this question comes under is countable sets and bijections, not sure if that helps or not.
In order to show that two sets have the same cardinality, you must show that there is a bijection between them. In your case, you must find a bijection between $\mathbb{R}$ and the set $(0,\infty)$; that is, a $1-1$ and onto function from $\mathbb{R}$ to $(0,\infty)$. For example, the function $e^x$ defined on $\mathbb{R}$ is an example: all of its values are in $(0,\infty)$, every positive value is attained, and no value is attained twice.