I was scrolling through this article on Wikipedia, and I was stumped when I came across this line:
Every real number greater than $0$ has two real square roots, so that the square root may be considered a multi-valued function. For exmaple, we may write $\sqrt{4}=\pm 2=\{2,-2\}$; although $0$ has only one square root, $\sqrt{0}=\{0\}.$
I very strongly believe that there is a conceptual gap that I need to bridge. I have always used the fact that the square root of a number is always positive (as seen by the graph of $y=\sqrt{x}$).
What particular fact am I overlooking?
As far as I understand upon reading the article again to look for clues, it is mentioned that the domain could be extended. So what I infer is that we can map $4$ under the (now multi valued) function $\sqrt{.}\; $to $-2$ and $2$ . Would I be right in saying so?