Page 2 of 2 FirstFirst 12
Results 16 to 25 of 25

Math Help - help with sequence prefixes

  1. #16
    Senior Member
    Joined
    Sep 2009
    Posts
    299
    I think my text defines it as starting from 0. In that case, sigma is {(0,0),(1,1)}. Then it is a prefix of tau according to your example. Am I wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #17
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774
    I would rather say, sigma, as defined above, is not a sequence.
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Senior Member
    Joined
    Sep 2009
    Posts
    299
    This is a summary of a definition of a sequence from my text:

    A sequence of n elements taken
    from set A is a function mapping from {0,1,2,...,n-1} to A. If
    we call the n elements a_1,a_2,...,a_n, then the sequence is the
    function that maps 0 to a_1, 1 to a_2, 2 to a_3, ..., and n-1 to
    a_n. Such a function, seen as a relation, is the set of ordered
    pairs {(0,a_1),(1,a_2),...,(n-1,a_n)}. E.g., the sequence <
    H,E,L,L,O >, is the set {(0,H),(1,E),(2,L),(3,L),(4,O)}.

    Does this change anything that you were saying?

    With this in mind I still can't come up with a proper counter example, nor can I understand your example properly.
    Follow Math Help Forum on Facebook and Google+

  4. #19
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,615
    Thanks
    1582
    Awards
    1
    Quote Originally Posted by Sneaky View Post
    Now I am confused with your previous statement with the example, so that still shows that its a subset but not a prefix? Or does there have to be a <0,0> in sigma, which then makes the example false?
    I truly mean you no disrespect by this comment.
    But this is an English language forum.
    As such, we have very clear definitions of terms.
    A sequence is a function from the positive integers to a field, real or complex.
    If the sequence \sigma_n is a subsequence of \tau_n then \sigma_n=\tau_{n_j} where n_1<n_2<\cdots<n_n.

    In that westernized context, can you reframe your question?
    If not, you need to find a forum that is compatible your language.
    Follow Math Help Forum on Facebook and Google+

  5. #20
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774
    Does this change anything that you were saying?
    No.

    It would be helpful if you posted this definition from the start. Such ubiquitous things as sequences often have slightly different definitions.
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Senior Member
    Joined
    Sep 2009
    Posts
    299
    OK, I'm just stuck with one thing, if you say it does not change anything you said before, and when when you say sigma is {<1,1>}, then according to the definition I posted, shouldn't it be the same as {<0,0>,<1,1>}?
    Follow Math Help Forum on Facebook and Google+

  7. #22
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774
    Quote Originally Posted by Sneaky View Post
    With this in mind I still can't come up with a proper counter example, nor can I understand your example properly.
    As I said earlier, if sequences as functions have to be defined on an initial segment of natural numbers, then being a subset is equivalent to being a prefix.
    Follow Math Help Forum on Facebook and Google+

  8. #23
    Senior Member
    Joined
    Sep 2009
    Posts
    299
    So technically with that definition of sequence, there is no counter example to show that sigma is a prefix of tau but not a subset. But if sequences don't have to be defined on an initial segment of natural numbers, then your example is a valid counter example.

    Is this right?
    Follow Math Help Forum on Facebook and Google+

  9. #24
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774
    Yes.

    Edit: In case sequences don't have to be defined on an initial segment, my example shows that being a subset does not imply being a prefix. For the other direction under the same definition, let sigma = {(1,0)} and tau = {(0,0), (1,1)}. Then sigma (representing the sequence <0>) is a prefix of tau (representing <0,1>), but is not a subset of tau.
    Follow Math Help Forum on Facebook and Google+

  10. #25
    Senior Member
    Joined
    Sep 2009
    Posts
    299
    OK, thanks.
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 4th 2010, 12:05 PM
  2. Replies: 2
    Last Post: March 1st 2010, 11:57 AM
  3. sequence membership and sequence builder operators
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: June 4th 2009, 03:16 AM
  4. Replies: 12
    Last Post: November 15th 2006, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum