3

I know what $x \in \{0, 1\}$, $x \in [0, 1]$, and $x \in (0, 1)$ mean. But recently I encountered $x \in \langle0, 1\rangle$. What does it mean?

Source: Problem 4760, Crux Mathematicorum 48.6, June 2022, pg 349. (PDF link via cms.math.ca). Transcribed in its entirety:

Proposed by Goran Conar.

Let $a_i\in\left\langle0,\frac12\right\rangle$, $i\in\{1,2,\ldots,n\}$ be real numbers such that $\sum_{i=1}^na_i=1$. Prove that $$n\sqrt{\frac{n-1}{n+1}}\leq \sum_{i=1}^n\sqrt{\frac{1-a_i}{1+a_i}}< (n+1)\sqrt{\frac{n-1}{n+1}} $$

Blue
  • 75,673
Occe1998
  • 31
  • 3
    Without additional context, this is a hopelessly open-ended question. Even the notations that you mentioned have multiple meanings depending on context. – Sammy Black Jul 19 '22 at 02:19
  • 3
    Without context, all I can do is make a wild guess. – Lee Mosher Jul 19 '22 at 02:20
  • 1
    Please provide more contexts to make your question clear. – RDK Jul 19 '22 at 02:22
  • One possibility: https://en.wikipedia.org/wiki/Inner_product_space – GEdgar Jul 19 '22 at 02:24
  • I think a couple of months ago I saw a question posted wherein the OP used $\langle a,b \rangle$ - or perhaps it was $\langle a;b \rangle$? - to refer to $[a,b]$ (as in a closed interval), so perhaps that's relevant. – PrincessEev Jul 19 '22 at 02:27
  • Edited to add source. – Occe1998 Jul 19 '22 at 02:31
  • 2
    Most likely, this is an unusual notation for open intervals. – Moishe Kohan Jul 19 '22 at 02:56
  • @MoisheKohan It's the notation that Norwegian high schoolers learn (presumably to distinguish it from coordinates; they also learn $\langle 0,\to\rangle$ for unbounded intervals, which is a convention I might actually find better than the usual, but they still learn $\displaystyle{\lim_{x\to\infty}}$ for some reason, because screw consistency). I was going to suggest it myself. – Arthur Jul 19 '22 at 03:06

0 Answers0