I agree that the sunrise example may not be the best one, I just wanted to show that definitions tend to become ambiguous when there are many disjunctive possibilities to get to roughly the same outcome.
Consider another probability question: “Conditional on me flipping this unbiased coin, will it land heads?”. My probability is 50%, I’m not an ideal Bayesian. But an ideal Bayesian would give a number very slightly less than 50% due to “edge” and “does not land” and other more exotic possibilities. If “epsilon” is a cop-out then is “50%” a cop-out?
It’s kind of the same example, what are the odds of the coin not landing either heads or tails? There are many possibilities, including those you listed, and it’s work if you care about this edge case (no pun intended). If you care about slight deviations from 50%, then do the work, otherwise just say “50% for my purpose”, no epsilon required.
I agree that the sunrise example may not be the best one, I just wanted to show that definitions tend to become ambiguous when there are many disjunctive possibilities to get to roughly the same outcome.
It’s kind of the same example, what are the odds of the coin not landing either heads or tails? There are many possibilities, including those you listed, and it’s work if you care about this edge case (no pun intended). If you care about slight deviations from 50%, then do the work, otherwise just say “50% for my purpose”, no epsilon required.