What word is used to describe an event that will never occur?

If an event happens a lot in a small window of time, it is considered frequent. If it does not, it is considered rare. What about a possible event that has never happened and which is expected never to happen? What word would describe the frequency of that event?

For example how would you answer this question: "How often does a nuclear war occur in your lifetime?"

Solution 1:

They are called impossible events or zero-probability events. You can see these terms in mathematics, physics, philosophy, and so on.

I can't think of anything besides never to describe such events in common parlance. But, depending on the context, asymptotic might prove a good fit.

P.S. As bib has mentioned in the comment below, the OP wants a possible event that has never occurred and will never occur. My suggestions might not qualify with this precondition. Then again, according to jwpat7, one of them might.

Solution 2:

I would go with "improbable", "highly improbable", or "statistically improbable" depending on the applicable situation.

Edit - Maybe something like, "It has not been observed and is considered highly improbable." This might cover what you described in your comment.

Edit2 - A little late on this one, but maybe scarcely? Or a good old fashioned hardly ever? Kind of synonyms for rarely, but seem slightly stronger

Solution 3:

Technically, the term is "zero probability". The classic mathematical example is throwing a dart with a tip of negligible width at a dartboard and expecting to hit a single mathematical point on the plane of that board. The point exists - it's defined - and therefore it is possible to hit it. However, there are so many (an infinite number) of other points that could be hit that, even given a well-aimed throw such that the chances of hitting a point on the dartboard is 1/1, the chances of hitting that exact point is 1/∞ = 0. Conversely, not hitting that single point is said to be "almost certain" in mathematical parlance.

Other terms that may fit:

practically impossible - this term allows for the technical possibility while still expressing the real-world impossibility.

infeasible - this is roughly synonymous with "improbable" or "unlikely", but has the connotation of "not doable", as in the action itself may be possible to accomplish, but the requirements involved behind the scenes to do it are prohibitive.

implausible - Again, technically possible, but the circumstances defy credibility.

However, remember the law of expected values; for any N, 1/N * N = 1. An infinitesimal chance, given infinite trials, is almost certain to happen once (there is always a mathematical chance that it will never happen on any N trials, but this chance approaches zero as N grows very large).

Solution 4:

To me, the idea itself seems like a contradiction. If an event is possible, but has never occurred and is expected never to occur, isn't it an impossible event? Any word that describes the frequency of an event will either acknowledge that it is possible (probability > 0) or that it isn't, ever (probability = 0).

Building off of Andrew Leach's comment, and looking for a term to go at the end of that continuum, what comes to mind is 'never occurring', though this is a term I pull out of nowhere, and is by no means official.

The probability term for an event where probability is exactly 0 is simply 'zero-probability event', but again, this is an impossible event.

EDIT: From jwpat's comment, that last sentence is incorrect. According to Wikipedia the correct term for a technically possible event with probability 0 is 'almost never'. (Am I right?)

Solution 5:

The secondary modifier (and negative emphasiser) vanishingly is available and accepted. It is defined at thefreedictionary, where examples of its use:

' "The probability that they coincide by chance is vanishingly small," said coauthor Alan Linde, also of Carnegie.'

and misuse:

'The number of complaints which are substantiated is vanishingly small....' (Huddersfield Daily Examiner) (even one is far from being a vanishingly small number)

are cited.

So we could use vanishingly rare (ie extremely rare); vanishingly probable (ie extremely IMprobable). (The latter term has been used by Richard Dawkins amongst others.)