1 divided by infinity equals zero (always?)

[njh]

TL;DR

1/ infinity = 0, but this seems a simplification.

I understand the mathematics that 1 divided by infinity is virtually zero and so equals zero. I look on the internet and that is the answer that I get. Is this a simplification for early mathematics learning and, if I continue, will I find a more complex answer? The reason that I ask is that I find this a simplification that does not sound right. Thank you.

 

[fresh_42]

You cannot divide anything by infinity since infinity isn't a number. The notation $1/\infty =0$ is a very sloppy way to write $\displaystyle{\lim_{n \to \infty}\dfrac{1}{n}=0}$ or whatever else goes to infinity. There is no division by infinity, only the remark that $\left|\dfrac{1}{n}-0\right|<\varepsilon$ gets arbitrarily small, but not zero.

 

[njh]

Thank you (and incidentally, my apologies for not using mathematical notation in my question).