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Quick convention question

  1. Nov 20, 2003 #1

    StephenPrivitera

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    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
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  3. Nov 20, 2003 #2

    Ambitwistor

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    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

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    [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

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    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
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