Dividing by square root of zero equals infinity?

Question

So, my calculator app produced a result that doesn't seem correct to me. According to my calculator, $\frac{1}{\sqrt{0}}=\infty$. By my understanding, $\sqrt{0}=0$ (since $0^2=0$). So, shouldn't $\frac{1}{\sqrt{0}}=\frac{1}{0}$ and therefore be undefined not equal to infinity?

Answer 1

Yes, it should be undefined. However, I should make you aware of the projectively extended real number system, where $+∞=-∞=∞$. $\frac{1}{0}$ is defined as $∞$. Here is a Wikipedia article about it: https://en.wikipedia.org/wiki/Projectively_extended_real_line