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I've found a couple symbols that include the concept of once, like "the list of values which appear only once" and stuff like that. Is there a symbol that just means "once" or "one repetition" or "single"? Like, "f() happens one time." (sorry if the combinatorics tag is off-base. I wanted to just use "symbols" but couldn't find a tag like that)

Matt
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1 Answers1

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$\exists!P(x)$ is defined to mean that there is only one occurrence where $P(x)$ is true.

It is called uniqueness quantification

Paul
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  • Usually "read" as "there exists unique $x$". – hardmath Apr 06 '16 at 14:21
  • That seems to be the closest to what the OP means. For all other usages of the word "once", one should not that it is certainly better to just use a concise and understandable natural language description with the word "once" than to introduce an obscure notation – Hagen von Eitzen Apr 06 '16 at 14:22
  • To be precise, the definition should read "there is one and only one", as "there is only one" could mean "there is zero or one " – Juho Kokkala Apr 06 '16 at 14:26
  • Yeah, but doesn't that mean that P(x) happens a lot and one of the happenings will be true, not that P(x) happens one time? – Matt Apr 06 '16 at 14:36
  • It would help a lot if you gave context to your question. What exactly do you want to write in mathematical terms? – Paul Apr 06 '16 at 14:40
  • @Matt In what sense do you intend "$P(x)$ happens" and "$P(x)$ is true" to be different? (This should be clarified in the question). – Juho Kokkala Apr 15 '16 at 16:09