I cant understand this liminf/sup definition

[transgalactic]

i got this new definition

http://img515.imageshack.us/img515/5666/47016823jz1.gif

what is the meaning of n>=0 under a sup.
sup is not a limit
its only a number
we can't put index under it
what is the meaning of this indexes?

 

[tiny-tim]

what is the meaning of n>=0 under a sup.
sup is not a limit
its only a number
we can't put index under it
what is the meaning of this indexes?

Hi transgalactic!

Under the sup is n ≥ 0, not n -> 0.

anything with a -> (such as n -> 0) would be a limit, as you know …

anything without a -> (such as n ≥ 0) means that that is the range over which the sup is taken …

in other words, if you rewrite it inside {}, then it finishes with : n ≥ 0}

 

[transgalactic]

i can't imagine what you are saying

can you rewrite the definition

 

[HallsofIvy]

"sup" is a property of a set. sup_{n\ge m} {a_n} is the supremum of the set {a_m, a_{m+1}, a_{m+2}, ...}.