disprove the following....? Don't worry, this is just a practice test, and I just need to understand how it works. So I need to prove or disprove:
(1) There is a subsequence S{n(k)} that converges to 2.
(2) There is a montonic supsequence of S{n} that decreases down to 3.
(3) S{n} is itself monotonic.
(4) If V{N} = sup {S{n} : n > N} then there exists numbers N,K such that V{N} = S{K}.
I have some ideas about these but they are vague and unfortunately the book doesn't have examples to work off of, just a bunch of abstract symbols, (which I sort of understand what they are trying to get at). Anyways, I could really use the help in understanding this.
Thanks,
Brian
(1) There is a subsequence S{n(k)} that converges to 2.
(2) There is a montonic supsequence of S{n} that decreases down to 3.
(3) S{n} is itself monotonic.
(4) If V{N} = sup {S{n} : n > N} then there exists numbers N,K such that V{N} = S{K}.
I have some ideas about these but they are vague and unfortunately the book doesn't have examples to work off of, just a bunch of abstract symbols, (which I sort of understand what they are trying to get at). Anyways, I could really use the help in understanding this.
Thanks,
Brian