Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time.
They may also have been referring to the fact that picking a random number over the whole number line is not that as simple as it sounds since the uniform distribution doesn't exist.
There is definitely a mathematical sense in which events with probability 0 can happen, but I don't know of any 'real-world' setting, e.g., in statistics, in which we correctly assign an event a probability of 0 (rather than just "too small to distinguish from 0") and yet find it happening. Could you give an example?
The mathematical sense you are referring to is "existence": the number you have picked does exist, but the probability of it being selected is zero.
Yes, I know. However, contravariant said (https://news.ycombinator.com/item?id=18174774):
> In statistics there's a slight difference between something that happens 100% of the time and something that always happens.
> Or rather just because something has a probability of 0 doesn't mean it can't happen, events with probability 0 happen all the time.
I took this to be a claim that there was a 'real-world' sense (or as real-world as statistics is), not just a strictly mathematical sense, in which events with probability 0 happen "all the time", and I was wondering what this sense (not the mathematical sense) was.
(Maybe that's the meaning of the perceived difference between the real world and statistics. Playing a lottery doesn't make sense, but people do win!)