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?

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- Feb 26th 2011, 08:32 AMRogueDemonPositive or Negative Infinity?

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? - Feb 26th 2011, 08:44 AMPlato
Have a look at this.

It appears that it depends on the side of 0 we choose. - Feb 26th 2011, 09:03 AMFernandoRevilla
- Feb 26th 2011, 09:35 AMNOX Andrew
I don't understand why .

- Feb 26th 2011, 09:49 AMFernandoRevilla
- Feb 27th 2011, 04:55 AMHallsofIvy
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.

Quote:

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.) - Feb 27th 2011, 05:34 AMNOX Andrew
You seem to have misquoted me. I understand the difference between negative infinity and infinity, just not the difference between positive infinity and infinity.

- Feb 27th 2011, 05:44 AMFernandoRevilla