Why is the range of reciprocal function $0$ and not the entire real number set? My reasoning is that, because the domain of the reciprocal function is $\mathbb R\smallsetminus\{0\}$ to avoid the undefined solution, why do we remove $\{0\}$ from the range even though it can take such value if the value of the element in the domain approaches infinity.
PS: I've not been taught the concept of limits yet, so please try to answer the question without making use of limits if this requires the use of any.