Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question on meaning of some symbols

  1. Sep 26, 2010 #1
    I don't know the meaning of these:


    1) [tex]sup_{B_\delta}|f(x,y)| [/tex]

    Where [itex]B_\delta [/itex] is the ball of radius [itex]\delta[/itex].

    2) [tex]\int \int _{R^2 \B _{\delta} } f(xy)dxdy[/tex]

    I don't know what is [itex]R^2 [/itex]\B[itex] _{\delta} [/itex]

    Please read my latex because the symbol really don't show correctly.
     
    Last edited: Sep 26, 2010
  2. jcsd
  3. Sep 26, 2010 #2

    Landau

    User Avatar
    Science Advisor

    1) The supremum of {|f(x,y)|} where (x,y) ranges over the ball centered at 0 of radius delta: |(x,y)|=sqrt(x^2+y^2)<delta.

    2) the plane R^2 without the ball centered at 0 of radius delta, i.e. \ (in Latex: "\backslash") means 'complement' or 'set difference'. So it consists of pairs (x,y) of real numbers such that |(x,y)|=sqrt(x^2+y^2)>=delta.
     
  4. Sep 27, 2010 #3
    Thanks for you reply, so for

    1) Is the upper bound of |f(x,y)| in the ball.

    2) Is the whole 2D plane minus the circle center at 0 with radius [itex]\delta[/itex]
     
  5. Sep 27, 2010 #4

    Landau

    User Avatar
    Science Advisor

    The least upper bound, a.k.a. the supremum ;)
    Yes.
     
  6. Sep 27, 2010 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No. There is no such thing as "the" upper bound of a set of numbers. If a set has an upper bound, then it has an infinite number of upper bounds. This is the least upper bound- the smallest number in the set of all upper bounds.

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Question on meaning of some symbols
Loading...