Searching through past posts I didn’t see anything specific to this. As I understand it, we can approximate what occurs when dividing by zero if you graph the function [y=1/x](https://i.imgur.com/MebU9l3.png) (ripped from google)
As X approaches zero, it becomes both infinity or negative infinity, which results in it being undefined.
Couldn’t positive or negative infinity be defined as the square root of infinity? or the square root of infinity squared? Obviously not all infinities are equivalent.
Thanks
Sincerely, a person who failed math
In: 0
The thing is that in math, you can define whatever you want.
So, you can define a function called squaring however you want. You can make it be a map from the set {all real numbers and +/- infinity} to itself (here infinity and -infinity are purely symbols) which sends -infinity and infinity to infinity. Under this map, the elements that gets sent to infinity is infinity and -infinity. In this sense, the squareroot of infinity is infinity and -infinity. You can also define a function called division, which takes in two elements of the set {all real numbers and +/- infinity}, and spits out another element in this set, however you want. You can make it so that 1 divided by 0 is the symbol infinity.
With these definitions, the square of (1 divided by 0) is infinity.
Such definitions aren’t always nice though. For example, with these definitions, some usual properties of arithmetic will need to be violated.
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