i got this 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 cant put index under it what is the meaning of this indexes?
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Originally Posted by transgalactic i got this 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 cant put index under it what is the meaning of this indexes? Remember that if is bounded then . The sequence, is non-increasing, therefore its limits is its infimum. Thus,
why you are saying that its not increasing its a supremum its only one number its the least upper bound of this sequence its a constant number it cannot increase or decrease. and then you are taking the great low bound of this constant number ???
Originally Posted by transgalactic why you are saying that its not increasing " alt="\sup \{ x_k | k\geq n\} " /> its a supremum its only one number its the least upper bound of this sequence its a constant number it cannot increase or decrease. and then you are taking the great low bound of this constant number ??? If is a bounded sequence which is non-increasing i.e. Then .
Originally Posted by ThePerfectHacker If is a bounded sequence which is non-increasing i.e. Then . ok i understood the last inf putting step. but why you are saying that 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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