1 divided by infinity equals zero (always?)

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.

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.

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