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I recently encountered the above notation for sets, and I've never encountered it before. What does it refer to?

abiessu
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user41281
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3 Answers3

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This is the notation for the open interval $(a,b)$.

Those two notations denote the same thing.

In case you do not know what an interval is, it is the set $\{x:a<x<b\}$ given an order relation $<$.

Hasan Saad
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    It is worth mentioning that this notation is popular in France, though not so popular in North America. – parsiad Sep 18 '15 at 14:37
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    Aha! So that is why we use it in Lebanon! – Hasan Saad Sep 18 '15 at 14:38
  • It's also common in Germany, although I remember it primarily from high school. I can't say if it's frequently used in university. – Barkas Sep 18 '15 at 14:39
  • Never used to use another notation here in Belgium. – Ruts Sep 18 '15 at 14:40
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    $]a,b[$ has some advantages over $(a,b)$ because $(a,b)$ can mean also an ordered pair or the coordinates of a point. Also it isn't coherent in geometrical notation. – user5402 Sep 18 '15 at 14:46
  • Dugundji used ]a, b[ as well as ]a, b] and [a, b[ in his topology book, which was the textbook for a course I took in the U.S.A. around 1966. – jbuddenh Sep 18 '15 at 15:00
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That just means the open interval $(a,b)$. The brackets facing to the other side should indicate that the borders $a$ and $b$ do not belong to the set.

Barkas
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$]a,b[$ is the set of numbers between $a$ and $b$ with $a$ and $b$ excluded. In symbols like Hasan Saad said $\{x:a\lt x\lt b\}$.

The opposite $[a,b]$ is the set of number between $a$ and $b$ with $a$ and $b$ included. In symbols $\{x:a\le x\le b\}$.

Ruts
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