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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?"

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    Are you asking for what comes at the end of a continuum? Constant - Frequent - Rare - ??? I'm not sure you can describe the frequency of something that has never happened; it's akin to dividing by zero. – Andrew Leach♦ Jul 31 '12 at 14:59
  • @AndrewLeach That's exactly what I asking. Constantly means it is always occurring, frequently means it is occurs alot, rarely means it almost never occurs. What if it actually never occurs? I know you can't divide by 0, but you can't divide by infinity either, yet there is a word ("constant") that represents a never ending frequency. – Rocky DeHart Jul 31 '12 at 15:12
  • You're looking for something between rarely and never. I'll keep thinking! – Ste Jul 31 '12 at 15:38
  • How about "near-never"? – Ste Jul 31 '12 at 15:39
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    An expression that comes to mind is not in a million years – Noah Aug 3 '12 at 23:09

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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.

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    The OP specifically said the event was possible even though it had not yet happened and likely never would. I think impossible and zero-probability don't fit. – bib Jul 31 '12 at 15:14
  • @bib hmm, good point. I reckon he will have to go to philosophy.se for that one :| I have no idea. – coleopterist Jul 31 '12 at 15:16
  • Yes for example: How often does a meteor strike earth in your lifetime? – Rocky DeHart Jul 31 '12 at 15:21
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    @RockyDeHart Never, because by the time they hit the ground, they’re by definition meteorites, not meteors. – tchrist♦ Jul 31 '12 at 15:25
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    "near-zero-probability" might work. They are exceptionally unlikely, but still possible. – Schroedingers Cat Jul 31 '12 at 15:26
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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

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    improbable does not describe frequency. For example: If someone asks "How often do you go to the gym?" You can reply "I go to the gym frequently" or "I go to the gym rarely" but you couldn't say "I go to the gym improbably". Which isn't even a word in that context. – Rocky DeHart Jul 31 '12 at 15:03
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    Good point. However, you could say, "It is improbable that I will go to the gym." I was just taking into account the comment a possible event that has never happened and is expected never to happen – degausser Jul 31 '12 at 15:09
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    @Rocky DeHart: I think you're mistaken. Obviously there's no concept of frequency as such for something that has never happened. But "statistically improbable" does at least imply that, along with the implication that it probably never will, either. – FumbleFingers Jul 31 '12 at 15:42
  • @RockyDeHart Would you mind showing the context of your desired sentence so we can help decide what exactly each usage would imply? – degausser Jul 31 '12 at 16:15
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    @RockyDeHart: I can only repeat that "frequency of occurrence" is almost a meaningless concept for something that never occurs. I suppose you might consider "infinitesimally low frequency" (doesn't occur in print that I can see, but there are 404 instances on the Net). – FumbleFingers Jul 31 '12 at 16:33
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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).

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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?)

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  • -1, as your answer is misleading. Zero-probability does not mean impossible; see links from google for probability zero does not mean impossible. A wordpress.com article is quite clear. – James Waldby - jwpat7 Jul 31 '12 at 16:18
  • I appreciate that my answer is technically misleading, and I can't really complain about the -1; but, this does raise the issue of just how technical an answer Rocky is looking for. In everyday situations, one wouldn't need to worry about the difference between a sure event and an almost sure event; I suppose that's why I answered the question in an 'English' sort of way. If Rocky wanted the official mathematical term, this question would almost be more suited to math. – Jesse M Jul 31 '12 at 17:46
  • I undownvoted after your edit. Yes, the wordings shown in the Almost surely article are correct. – James Waldby - jwpat7 Jul 31 '12 at 20:57
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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.)

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In medical circles, they have become known as never events, as they should never happen. This is not the same as probably won't ever happen, but it sounds like it could fit your purpose too.

Go ahead and coin a new use for a term :)

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  • I saw this mention of 'never events' too while I was searching! Though the term isn't related to probability right now, it is a useful term that could have an application outside of the medical practice: any event that is technically possible, but should never occur. It would be nice to have a term for that :) – Jesse M Jul 31 '12 at 15:30
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Given that you've asked for a frequency, you've answered you own question: zero- frequency event.

Within a given window of time, event occurs:

  • Many times --> Frequent
  • Moderate number of times --> moderately frequent
  • Small number of times --> infrequent
  • Very small number of times --> very infrequent
  • Zero times --> zero frequent

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

But ... I'm not sure your nuclear-war example works as intended. First, my lifetime isn't over. Second, there will be many other lifetimes after mine, I hope. Third, to talk about frequencies, we have to assume that no nuclear war will wipe us all out, so that, for example, we can talk about the frequency of nuclear wars, e.g., the number of nuclear wars per millennium or per 106 years.

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  • Actually, a millennium is 10³ years. – Scott Aug 29 '16 at 5:09
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A purple unicorn.

A unicorn being, mythically, something so extraordinary that one would never get to see it, coupled with the added distinction of ‘purple’ - making it even more rare and thus impossible to ever be seen.

So I think if you describe your event as a ‘purple unicorn’, people will get that it is too extraordinarily rare for it to ever actually occur.

https://www.unicornsrule.com/purple-unicorn/

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These are "black swan" events. You (and everybody you take seriously) think the events have an extremely low probability of occurring. But if such an event does occur, you might need to radically revise your odds estimates.

Nassim Taleb popularized the concept. Europeans knew about swans -- they were (and are) beautiful birds. Every swan in Europe was white, so Europeans understandably thought that all swans were white. But one day, European explorers found a place halfway around the world that had a black swan. And as you might guess, the black swan had many relatives, who were also black.

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I’d go with “fallacy”. If the event is certain of happening, it’s a “tautology”.

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  • -1 for? Mathematically, a fallacy is something that's ever true – notablytipsy Jul 31 '12 at 17:46
  • Mathematical logician here. A fallacy is not a statement that is never true (negation of a tautology without free variables) but an invalid argument. In fact, when you express a fallacy as a formula with free variables (common practice, as for tautologies), it may be accidentally true depending on their values. Besides, the question is not about logical statements but about events. The fact that one can sometimes be modeled by the other still doesn't make it intuitive to transfer terminology outside a context that does this - not for mathematicians, and certainly not in ordinary language. – user86291 Oct 25 '15 at 16:08

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