![infinity number infinity number](https://res.cloudinary.com/dzawgnnlr/image/upload/v1589820522/Number-Line.png)
If x takes on only negative values, it becomes negatively infinite, in which case we write When the variable is x and takes on only positive values, then x becomes positively infinite. We say that a variable "becomes infinite" or "tends to infinity" if, beginning with a certain term in a sequence of its values, the absolute value of that term and of any subsequent term we name is greater than any positive number we name, however large. See this from Wikipedia, especially the views of Carl Friedrich Gauss in the section "Reception of the argument."ĭ EFINITION 4. The student should be aware that the word infinite as it is used and has been used historically in calculus, does not have the same meaning as in the theory of infinite sets. So when we say that the limit is infinity, we mean that there is no number that we can name. We say that as x approaches 0, the limit of f( x) is infinity. We then say that the values of f( x) become infinite, or tend to infinity.
![infinity number infinity number](https://gofiguremath.org/img/Hilbert-Infinity-Buses.jpg)
No matter what large number we name, it will be possible to name a value of x such that the value of f( x) will be larger than that number we named. Then as the values of x become smaller and smaller, the values of f( x) become larger and larger. When we say in calculus that something is "infinite," we simply mean that there is no limit to its values. I NFINITY, along with its symbol ∞, is not a number and it is not a place.