A quick question on notation interpretation

[michonamona]

Hello,

How is the following notation read?


$$(a_n)$$ is a bounded sequence. Let$$y_n = sup(a_k : k\geq n)$$


What is meant by $$k\geq n$$?

Thank you for your help.

M

 

[snipez90]

Seems like you're dealing with limsups. Basically

$$y_n = \sup \{a_n, a_{n+1}, a_{n+2}, ...\},$$

so that

$$y_1 = \sup \{a_1, a_2, a_3,... \}$$
$$y_2 = \sup \{a_2, a_3, a_4,... \}$$

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.

 

[michonamona]

ah... thanks!