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!

Quick convention question

  1. Nov 20, 2003 #1

    StephenPrivitera

    User Avatar

    Is the closed interval [a,a] considered a legitimate notation for the set {a}? Would (a,a) denote the empty set?
     
    StephenPrivitera, Nov 20, 2003
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Nov 20, 2003 #2

    Ambitwistor

    User Avatar

    I haven't actually seen anyone use that notation in such a degenerate case, but I don't see any reason why the usage you describe isn't legitimate.
     
    Ambitwistor, Nov 20, 2003
  4. Nov 20, 2003 #3

    HallsofIvy

    User Avatar
    Science Advisor

    [a,a] is used- usually in something like [a,b] where you want to consider the possibility that b= a.

    If I came across reference to an interval like (a,a), I probably would interpret it as the empty set- although I would wonder why they picked a!
     
    HallsofIvy, Nov 20, 2003
  5. Nov 21, 2003 #4

    StephenPrivitera

    User Avatar

    A={x : f(x)<0 on [a,x]}
    Is a in A? It is if f(x)<0 on [a,a]. And since [a,a] has only one number, it suffices to show that f(a)<0.

    A={x : f(x)<0 on (a,x)}
    Is a in A? It is if f(x)<0 on (a,a). But this is kind of nonsense. There is nothing in (a,a). You make the call.

    So anyway, I just wanted to point this out to show why you might write (a,a) rather than {}.
     
    StephenPrivitera, Nov 21, 2003
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook