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Upper limit of a sequence

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Let $s_n$ be a sequence of real numbers and define $E$ to be the set of all subsequential limits of $s_n$ in the real extended line. Then we define the following

\(\displaystyle \lim \text{sup } s_n = \text{sup } E\)​

For some reason I don't quite understand the above formula , do we need to prove it ? It would be nice if you give some examples.
 

Plato

Well-known member
MHB Math Helper
Jan 27, 2012
196
Let $s_n$ be a sequence of real numbers and define $E$ to be the set of all subsequential limits of $s_n$ in the real extended line. Then we define the following
\(\displaystyle \lim \text{sup } s_n = \text{sup } E\)​
For some reason I don't quite understand the above formula , do we need to prove it ? It would be nice if you give some examples.
We really don't prove a definition. There are many equivalent ways to define lim sup.
But there is no point in reinventing the wheel. Have a look at this page.
 
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