Results 1 to 4 of 4

Math Help - Definition of a sequence

  1. #1
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597

    Definition of a sequence

    My book has the attached definition. Could someone explain to me in English what the bottom part is saying please?

    Any input would be greatly appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Definition of a sequence-temp.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433
    The intuitive meaning of "a sequence a_n converges to a limit L" is that the farther out in the sequence you look, the closer the values get to L, and more specifically, if we look far enough out in the sequence, the values get as close as we want to L (and stay at least that close forever after).

    The integer N in the definition represents how far out we're looking in the sequence--that's why it says "when n>N". What the definition is really saying is: "tell me how close you want the values of the sequence to be to L, and I'll give you a number N, so that every value, after the Nth value, is at least that close to L".
    Follow Math Help Forum on Facebook and Google+

  3. #3
    s3a
    s3a is offline
    Super Member
    Joined
    Nov 2008
    Posts
    597
    What about that inequality with the epsilon though?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2010
    Posts
    65
    Quote Originally Posted by s3a View Post
    What about that inequality with the epsilon though?
    The epsilon is how close you need the sequence to be to L. The definition is saying we can pick any positive epsilon arbitrarily small and we can find an N so that when we get to n>N in the sequence, the sequence is closer than epsilon to L.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. definition of convergence of a sequence
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 23rd 2011, 12:04 PM
  2. Convergence of sequence using the definition
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: August 2nd 2010, 08:47 AM
  3. Definition of sequence to infinity
    Posted in the Differential Geometry Forum
    Replies: 24
    Last Post: January 20th 2010, 08:04 AM
  4. confused with sequence definition !
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 4th 2009, 09:05 PM
  5. Definition of a sequence of elements in a set?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 5th 2007, 12:11 PM

Search Tags


/mathhelpforum @mathhelpforum