I came across this answer, written over a year ago, to a question about division by zero. The answer was written by a Physics instructor who seems to be rather confused.
- Division by zero is often defined as infinity. Infinity divided by zero is infinity-squared. For signs to be defined correctly, you must have a +0 and a -0. This is often accomplished through the theory of limits. The limit of x as x approaches zero from the negative side is -0. The limit of x as x approached zero from the positive side is +0. Higer (sic) level mathematics uses the concept of infinity quite often.
Let’s gloss over the first two appalling sentences. In the following sentences I suppose he is trying to refer to the fact that one can approach 0 (or any number) from different directions. If x approaches 0 from above, that is x remains positive, then you can write, for example, . Note that the limit is written as 0 not +0 which is of course equal to 0 so there’s no point writing it! This notation allows one to show that different things can happen if x approaches 0 from above or from below and to say that if and only if (where f is a real-valued function defined on a neighbourhood of 0).
Personally, I like using and rather than and respectively, because they illustrate the approach from above or below.