Is the answer to this question positive or negative infinity? The calculator at Online Limit Calculator gives positive infinity, but wouldn't -4/0 be negative?
Strictly speaking, that limit does not exist, even as "plus infinity" or "negative infinity"! The two one sided limits are
(for example, if x= 0.0001, and
(for example, if x= -0.0001, [tex]= -.0005+ 40000= 39999.9995.
I was sorely tempted to ask if you understood why !I don't understand why .
Of course, neither " " nor " " is actually a number. We are really talking about limits of functions or sequences. and are different because sequence that converge to each, such as 1, 2, 3, 4, ..., n, ..., which has limit , and -1, -2, -3, -4, ..., -n, ..., which has limit , are clearly getting farther apart so cannot converge to the same thing.
(From a "topological" viewpoint, adding and "compactifies" the real number line making it topologically equivalent to a closed interval. Given any topological space, we can always find its "one point compactification", adding a single point, and "open" sets containing that one point, to make it compact- However, it changes the topological properties of the space much more than the "Stone-Chech compactification" above. If we did that with the set of real numbers, we would get a single "point at infinity" but now the it would be topologically equivalent to a circle rather than a line segment.)