Proof of $+\infty=-\infty$ (Maybe) I guess we can agree that $+0 = -0$. Now, after that, I was simply looking at some graphs. The graph of $\tan x$ shows asymptotes at x = $n\pi + \pi/2$. I got to thinking, what if they weren't asymptotes, but actually continuous lines? If I take $0$ and ($+/-$)$\infty$ as diametrically opposite points of a circle, and sort of roll the $\tan x$ graph into a cylinder with the Y-axis as circumference and x-axis as the length of the cylinder, then $\tan x$ will become continuous. This seems intuitively valid, but is there a formal proof possible that $+\infty=-\infty$? (Using simple mathematics, if possible. I am still in Grade 11)

In general (for grade 11), remember that $\infty$ is not a real number. To say that two elements are equal, they need to be equal in some set. That is, they need first be elements in some set. And $\infty$ is not an element in the set of real numbers.

For example, when we say that a limit (of a function) is (equal to) $\infty$ or $-\infty$, all we are saying is that the values of the function can be made as large (positive or negative) as we would like. So, it can be a bit confusing to talk about a limit being _equal_ to $\infty$ because it gives the impression that $\infty$ is a number.

Does that mean we never ever talk about $\infty$ as a number (or element in a set)? No, for more on this see for example

* What is the result of infinity minus infinity?
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