how much is plus infinity minus infinity

Answer

You cannot calculate the indefiniteness “infinity minus infinity”. That is why we call it an indefinite form. The simplest reason to see that you can’t give a good answer to the question “how much is infinity minus infinity” is the following. You could say that “infinity minus infinity” equals 1 because “1 plus infinity” equals infinity. But for the same reason, you could argue that “infinity minus infinity” equals 27 or any other number.

In analysis, there is another reason why we call “infinity minus infinity” indeterminate. After all, if x_n and y_n are rows that both converge to infinity (for example, the rows n and n+1), then with the row x_n – y_n still happen. This sequence may converge (to an unpredictable limit) or may not converge at all.

All this is in contrast to the “definite form” which says that “infinity plus infinity” equals infinity. With the rows x_n and y_n as above, will x_n + y_n always converge to infinity.