1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Just a Yes or No Question

  1. Sep 10, 2008 #1
    Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?
  2. jcsd
  3. Sep 10, 2008 #2
    ]-∞, ∞[

    Never seen it written like that I would be more inclined to write :
    [-∞, ∞] or more commonly me thinks (-∞, ∞) - to show that this is open

    When you write -∞<x<∞ I guess the most common assumption is that x is contained in the reals but without context it really isn't smart to assume anything. Usually someone will specifically state x contained in the reals and -∞<x<∞ - or x contained in the integers and -∞<x<∞ or the set that x belongs to will be clear from the context.

    (Sorry for not responding with yes or no but hopefully you understand why I could not)
  4. Sep 10, 2008 #3
    If the brackets are facing outwards ][ then they're supposed to mean the points are excluded.
    If the brackets are facing inwards [] then they're supposed to mean the points are included.
    At least, that's what I was told, and that's what I read in my textbook.

    Anyway, yes, I see your point. Another number with the answer of "all real numbers" simply showed the symbol for it, so I'm pretty wary of assuming that -∞<x<∞ means "all real numbers" as well.

    Thank you for your input though. :)
  5. Sep 10, 2008 #4
    I think the ] [ notation is used in other countries other than US.
  6. Sep 10, 2008 #5


    User Avatar
    Staff Emeritus
    Science Advisor

    In general, I'd say yes. But, it's normally easier to write something like [itex]x\in\mathbb{R}[/itex]
  7. Sep 10, 2008 #6
    Must be, in the US we typically use () to show open, and [] to show closed.
  8. Sep 10, 2008 #7
    yes that's exactly what that notation means and pretty much the only legit use of the symbol ∞
  9. Sep 11, 2008 #8
    Aaaah, thanks. I asked my math teacher before I read the last few posts, and confirmed that the answer is yes as well. :)
  10. Sep 11, 2008 #9
    You say

    Does ]-∞, ∞[ (can also be written as -∞<x<∞) mean all real numbers?

    first of all there is a difference between ]-∞, ∞[ and -∞<x<∞, the first is all the real numbers, the second is the same as [itex]x \in ]-∞, ∞[ [/itex]. You are right that ]-∞, ∞[ is all the real numbers, but an interval is defined from the real numbers, so that notation is rarely used.
  11. Sep 11, 2008 #10
    the itex tags are misrepresenting your point. I view it as x in ] -8743, 8743 [

    But what you actially wrote was x \in ]-∞, ∞ [ with itex tags.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook