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What do you call an event that occurs only once in its environment?

For instance, birth and death are two events that occur only once in the lifetime of a living thing.

I am looking for a word or phrase that would be synonymous to "non-repeating".

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up vote 4 down vote accepted

Consider the following:

One-time, one-off, one-shot, singleton, nonce.

Some other perhaps-less-suitable words suggested in Antonym of "recurrent" [closed] include

isolated, seldom, infrequent, non-periodic.

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Be aware that 'nonce' in this sense is archaic, but is modern UK slang for a sex offender. – Mynamite Apr 2 '13 at 23:00
In the computer science field, “nonce” is a well-known and commonly-used word that means a one-off item, in terms like “a nonce word” or “a nonce variable”. That is, I disagree that it's “archaic” (but agree with your other remark about nonce) – jwpat7 Apr 2 '13 at 23:23
Yes, I take it back, I looked around a little and found it was more common than I realised. I was thinking more of Shakespeare's use 'for the nonce'. jwpat7, I'm trying to add your name into this comment but it's not accepting it. – Mynamite Apr 2 '13 at 23:27
Try using any of those words followed by "event". Which word do you think would be most suitable? An illustrative sentence would be much appreciated. – KeyBrd Basher Apr 3 '13 at 5:31
How about 'unique'? I would say "one-off event" for something like a celebration/anniversary/sporting occasion, or "once-in-lifetime" [experience/chance to do something]. "Isolated" has negative overtones - "Without proper supervision the children ran riot. This was an isolated event and won't be allowed to happen again." ('isolated incident' would be better expression to use here). Neither of these would be suitable for 'birth' or 'death'. – Mynamite Apr 5 '13 at 10:03

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