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I see this class of numbers all the time, so I was wondering if there was a special name for it.

How to refer to a number $n$ in $\Bbb R$, such that $0<n<1$?

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    $\begingroup$ Often "the open unit interval." $\endgroup$
    – Andrew
    Nov 6, 2012 at 18:20
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    $\begingroup$ And $0 > n < 1$ is probably not what you meant. $\endgroup$
    – TMM
    Nov 6, 2012 at 18:21
  • $\begingroup$ yes, my mistake for that. $\endgroup$
    – Zchpyvr
    Nov 6, 2012 at 22:57
  • $\begingroup$ Two related questions. $\endgroup$ Nov 8, 2012 at 15:00
  • $\begingroup$ This question keeps popping up, and my conclusion is that there just isn't a good and well-established English name for these numbers. So for my own coding, I'm making up my own word: unidecimal. $\endgroup$
    – Kal
    Mar 10, 2022 at 22:54

1 Answer 1

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The set of all such numbers is $\{x \in \Bbb{R} \mid 0<x<1\}$, which is also more simply denoted $(0, 1)$, and occasionally, as: $\;]0, 1[\;$.

As Andrew pointed out, it is often referred to as "the open unit interval".

(One could say that the unit interval is to the real numbers what the unit circle is to the complex numbers, so to speak.)

One reason the values in the unit interval come up a lot is that the open unit interval is often used as an exemplar/representative of the real numbers, what can be said of the open unit interval can often be said of the set of real numbers, and vice versa. In terms of set theory, the cardinality of the unit interval of real numbers is equal to the cardinality of the real numbers; there exist bijections between the unit interval and the set of real numbers. And the range of probability is usually encompassed by the (closed) unit interval. So yes, it comes up a lot...

If you are asking whether there is some common name for referring to some particular element $x \in \Bbb{R}$, such that $0<x<1$ (i.e. if you are asking for the name an element of the set $(0,1)$ ...):

Then I would simply refer to $x$ as "an element in the open unit interval (of $\Bbb{R}$)" and you could simply denote such an element by writing $x\in (0,1)\subset \mathbb{R}$.

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  • $\begingroup$ I certainly didn't exhaust all the ways and domains in which the unit interval is an exemplar...! $\endgroup$
    – amWhy
    Nov 6, 2012 at 18:44
  • $\begingroup$ In response to that last question; I meant the name for the numbers in the open unit interval. Just as there is the real number set, the numbers in that set are called the real numbers. Would I just denote them as open unit interval numbers? Sounds a bit awkward. $\endgroup$
    – Zchpyvr
    Nov 6, 2012 at 23:00
  • $\begingroup$ ahh... I see. Well, I learned something new today. Thank you! $\endgroup$
    – Zchpyvr
    Nov 6, 2012 at 23:19
  • $\begingroup$ @zchpyvr My pleasure! $\endgroup$
    – amWhy
    Nov 6, 2012 at 23:22

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