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A quick question on notation interpretation

  1. Mar 23, 2010 #1
    Hello,

    How is the following notation read?


    [tex] (a_n)[/tex] is a bounded sequence. Let[tex] y_n = sup(a_k : k\geq n) [/tex]


    What is meant by [tex] k\geq n [/tex]?

    Thank you for your help.

    M
     
  2. jcsd
  3. Mar 23, 2010 #2
    Seems like you're dealing with limsups. Basically

    [tex]y_n = \sup \{a_n, a_{n+1}, a_{n+2}, ...\},[/tex]

    so that

    [tex]y_1 = \sup \{a_1, a_2, a_3,... \}[/tex]
    [tex]y_2 = \sup \{a_2, a_3, a_4,... \}[/tex]

    etc.

    In your notation, the k is just a dummy variable that tells us that all terms of the sequence (a_n) from the n-th term forward is included in the set in which we take the supremum of to get y_n.
     
  4. Mar 24, 2010 #3
    ah... thanks!
     
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