The word 'epsilon' is useful in such cases; it means 'nearly zero' or 'too close to zero to calculate'.
"Negligible" is a much better word, in my opinion, since epsilon is (conventionally) an arbitrarily small number, not a sufficiently small number. You could use "infinitesimal", but nothing in reality is actually infinitesimally small (including probabilities), so again you'd be inaccurate. I always get frustrated when people misuse precise mathematical words that have lots of syllables in them. The syllables are there to discourage colloquial use! I don't mind if you try to show off your knowledge, but for heaven's sake don't screw up and use that precise brainy term wrong!
You're straddling a strange line here. You're demanding a certain amount of strictness that is itself short of perfect strictness.
There's no such thing as an "arbitrarily small number". There are numbers chosen when any positive number might have been chosen. In particular, a given epsilon need not be "negligible". Really, to conform to the strict mathematical usage, one shouldn't say "epsilon" without first saying "For every". Once you're not demanding that, you're not using the "precise mathematical words" in the precise mathematical way.
I'm not saying that you're on some slippery slope where anything goes. But I wouldn't say that AdeleneDawner is either.
I would like to propose this as a thread for people to write in their predictions for the next year and the next decade, when practical with probabilities attached. I'll probably make some in the comments.