First off, sorry if this is in the wrong section.
The question goes...
We define a sequence by . Find an increasing list of numbers , so that the subsequence tends to 1. Prove that does not tend to a limit.
I have no clue. I hate stuff like this.
Okay, I have a similar example with a solution, but I don't understand it either.
We define a sequence by .Find an increasing list of numbers , so that the subsequence tends to 0. Prove that does not tend to a limit.
The answer for the first bit says...
A subsequence where the value is zero is given by , so ...
Why though?
The answer to the second bit it says...
To prove the sequenece does not tend to a limit, we have to find a subsequence where the limit is not zero. Take , then . Now we say, if the sequence tend to a limit , then so do the subsequences, hence , which is a contradiction, hence the assumption tends to a limit is false, and the sequence does not tend to a limit.
Why ? And why does ? I just don't get it.