Notices
Results 1 to 7 of 7
Like Tree5Likes
  • 1 Post By Guitarist
  • 1 Post By phyti
  • 1 Post By Guitarist
  • 1 Post By Strange
  • 1 Post By Guitarist

Thread: The Sequences

  1. #1 The Sequences 
    Forum Freshman
    Join Date
    Dec 2012
    Posts
    76
    Excuse me ... .



    We can seem guess the next terms in the sequence, say, ... .

    Maybe, we will say that the next terms is ... .

    But, in fact, in real line, we cannot guess the next term, because the next terms is not unique ... .

    Really, the next term is undeterminated ... .

    We can make various patterns by the method, called interpolation ... .


    ...


    Let, the sequence ... .

    We are asked to guess the next terms ... .

    The interpolation is such that :



    where :

    is fixed function,

    are unknown constant ... .

    In this method, we must substitute the sequence to the pattern of interpolation ... , and ... find all ... .



    If we are given the pattern of the sequence, however, we can guess the next terms ... .



    Thank you very much for the attention ... .


    Last edited by trfrm; December 10th, 2012 at 09:02 PM.
    Reply With Quote  
     

  2.  
     

  3. #2  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,623
    I am sorry to appear rude, but this is a terrible muddle.

    Let's see.....,.,We assume the existence of the natural numbers , also known as the "counting numbers"

    We assume 2 properties of this set

    1. There exists a least element in which by convention one calls as 1

    2. We assume that every has a successor element denoted by

    Then, given an arbitrary set , then the mapping defines a sequence in such that is, by convention written as for all

    Thus the sequence .

    So given , say, how hard is it to guess the next element in the sequence?

    Your problem stems from the fact that you fail to distinguish between domains and codomains


    trfrm likes this.
    Reply With Quote  
     

  4. #3  
    Forum Freshman
    Join Date
    Jun 2006
    Posts
    94
    Quote Originally Posted by Guitarist View Post
    I am sorry to appear rude, but this is a terrible muddle.

    Let's see.....,.,We assume the existence of the natural numbers , also known as the "counting numbers"

    We assume 2 properties of this set

    1. There exists a least element in which by convention one calls as 1

    2. We assume that every has a successor element denoted by

    Then, given an arbitrary set , then the mapping defines a sequence in such that is, by convention written as for all

    Thus the sequence .

    So given , say, how hard is it to guess the next element in the sequence?

    Your problem stems from the fact that you fail to distinguish between domains and codomains
    You are not rude, but presumptuous.
    The poster didn't specify the set of natural numbers. You are assuming this. The integers 1,2,3,4,5 could be a random sequence, or one from an unlimited number of algorithms.
    Unless you specify the algorithm/function used to select the sample, you cannot know what the next element will be.
    trfrm likes this.
    Reply With Quote  
     

  5. #4  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,623
    phyti, which part of the word "defines" do you not understand?

    If you had access to a half decent text, you could quickly find that the definition I gave is perfectly standard. As you quite obviously don't, I can only assure you that it is standard
    trfrm likes this.
    Reply With Quote  
     

  6. #5  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    I think what trfm is trying to say is that given an initial sequence, you might assume it is the beginning of the set of natural numbers (say) but actually it is an arbitrary sequence which just happens to start like that.

    In other words, what is the next item in: 1, 2, 3, 4 ?

    Any sane person would say, 5.

    But no! The answer is "elephant"

    What is the point of this thread? Is it a joke of some sort?
    trfrm likes this.
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  7. #6  
    Forum Freshman
    Join Date
    Dec 2012
    Posts
    76
    Quote Originally Posted by Guitarist View Post
    phyti, which part of the word "defines" do you not understand?

    If you had access to a half decent text, you could quickly find that the definition I gave is perfectly standard. As you quite obviously don't, I can only assure you that it is standard
    I'm sorry ... . I forgot to add the set of real numbers ... . I have corrected my previous post ... .

    Thank you for your correction ... .


    Quote Originally Posted by Strange View Post
    I think what trfm is trying to say is that given an initial sequence, you might assume it is the beginning of the set of natural numbers (say) but actually it is an arbitrary sequence which just happens to start like that.

    In other words, what is the next item in: 1, 2, 3, 4 ?

    Any sane person would say, 5.

    But no! The answer is "elephant"

    What is the point of this thread? Is it a joke of some sort?
    It's maybe ... because the elephant is an elemen of a set of everything ... .
    Reply With Quote  
     

  8. #7  
    Moderator Moderator
    Join Date
    Jun 2005
    Posts
    1,623
    Quote Originally Posted by trfrm View Post

    It's maybe ... because the elephant is an element of a set of everything ... .
    Yeah well, you need to be very careful here.

    Let me explain, using as little mathematical notation as clarity permits, as it appears you not mathematically sophisticated (this is not a criticism BTW, simply an observation).

    So suppose there exists a set of everything, which I can call . Then the set of elephants is obviously a subset of . And so is the set of "things" that are definitely NOT elephants. The set of elephants is a subset of mammals, also a subset of , and so is the set of "non-elephant" mammals.

    Both these sets are subsets of a subset of which we may call "life forms", and so is the set of "non-life forms".

    Continuing in this fashion, assuming you haven't already lost the will to live, we arrive at the conclusion that the set of everything contains as a subset all those "things" that are not members of .

    This a contradiction known as Russell's Paradox
    trfrm likes this.
    Reply With Quote  
     

Similar Threads

  1. Number sequences
    By Ascended in forum Mathematics
    Replies: 15
    Last Post: May 18th, 2012, 03:03 PM
  2. Applying sequences to non-integers
    By brody in forum Mathematics
    Replies: 2
    Last Post: January 1st, 2012, 06:29 PM
  3. Sequences with infinitely many acc points
    By VnnE4aEXxfhkrjPX in forum Mathematics
    Replies: 6
    Last Post: October 9th, 2011, 02:17 PM
  4. Short exact sequences.....
    By Guitarist in forum Mathematics
    Replies: 2
    Last Post: November 18th, 2008, 06:45 AM
  5. Sequences
    By PPonte in forum Mathematics
    Replies: 1
    Last Post: May 24th, 2006, 02:15 PM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •