regarding this defintion(adsbygoogle = window.adsbygoogle || []).push({});

http://img515.imageshack.us/img515/5666/47016823jz1.gif [Broken]

i was told that

Remember that if [itex]x_n[/itex] is bounded then [itex]\limsup x_n = \lim \left( \sup \{ x_k | k\geq n\} \right)[/itex].

The sequence, [itex]\sup \{ x_k | k\geq n\}[/itex] is non-increasing, therefore its limits is its infimum.

Thus, [itex]\limsup x_n = \inf \{ \sup\{ x_k | k\geq n\} | n\geq 0 \} [/itex][/quote]

i cant understand the first part

why he is saying that

[itex]\sup \{ x_k | k\geq n\}[/itex]

is not increasing.

you are taking a bounded sequence and you get one number

which is SUP (its least upper bound)

thats it.

no more members

??

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# Homework Help: I cant understand this explanation of limsup

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