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A quick question on notation interpretation

  • #1
122
0
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
 

Answers and Replies

  • #2
1,101
3
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.
 
  • #3
122
0
ah... thanks!
 

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