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.
You're demanding a certain amount of strictness that is itself short of perfect strictness.
Actually, I'm fine with people speaking vaguely, I just don't want to see terminology misused.
There's no such thing as an "arbitrarily small number".
"Through adding zeroes between the decimal point and the 7 in the string '.7', the number we are representing can be made arbitrarily small." Is this a misuse of the word "arbitrarily"?
...In particular, a given epsilon need not be "negligible". Really, to conform to the stri
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.