Why is divide by zero not the square root of infinity?

Question

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

Answer 1

No. Infinity is a concept not a number. And you can’t divide anything into groups of nothing. Since infinity isn’t actually a number talking about it’s square root is nonsensical.