- #1

- 122

- 0

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

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- Thread starter michonamona
- Start date

- #1

- 122

- 0

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

- 1,101

- 3

[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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