topology 3....

From: mina_world (mina_world_at_hanmail.net)
Date: 09/30/04 

Date: Fri, 1 Oct 2004 00:31:41 +0900

hello....doctor

suppose that
(X,d) is metric space.
sequence {x_n} converges to x.
y in X

show that
for all positive integer n,
there exists positive number M such that d(y, x_n) <= M

------------------------------------------------
um.....i can't.......

i can't make the relation between y and x_n.

help me, please.

thank you very much for your advice.

Relevant Pages

  • Re: Do any integers occur in both sequences?
    ... term for term you end up with a pattern progression. ... Where each even negation progresses by one followed ... sequence to generate the smaller ...
    (sci.math)
  • Re: sum{k>=m} floor(n/k) = n
    ... Consider the sequence A145265 of the On-Line Encyclopedia Of Integer ... A positive integer n is included if there exists a positive integer m ... then the sum will be of 1's and 2's and some number ...
    (rec.puzzles)
  • Fibonacci connection between Huffman codes and Wythoff array
    ... Given a sequence of n positive weights P=. ... The Wythoff array is shown below, to the right of the vertical colon line. ... A sequence Pmin of n positive integer weights is called ... A minimizing absolutely ordered sequence of the maximum height Huffman tree T ...
    (sci.math)
  • Re: topology 3....
    ... > is metric space. ... > sequence converges to x. ... > for all positive integer n, ... Apply the triangle inequality to x_n, x and y and see what you get ... ...
    (sci.math)
  • General Sum-Counting Result
    ... "In One Sequence Or Another " ... Let r be a positive integer. ... monotonically increasing function. ... and we sum over all r-tuples of positive integers ...
    (sci.math)