Results 1 to 4 of 4

Math Help - List the elements of S produced by the first five applications of the recursive defin

  1. #1
    Junior Member
    Joined
    Apr 2013
    From
    USA
    Posts
    69
    Thanks
    1

    List the elements of S produced by the first five applications of the recursive defin

    Let S be the subset of the set of ordered pairs of integers
    defined recursively by



    Basis step: (0, 0) ∈ S.


    Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S
    and (a + 3, b + 2) ∈ S.


    a) List the elements of S produced by the first five applications
    of the recursive definition.

    How do I know which (a,b) pairs to use? I know that it's the first five but I don't know how to get the first five.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780

    Re: List the elements of S produced by the first five applications of the recursive d

    Taken from this thread.

    the recursion step forms two new pairs. So, at each step you could also form (a + 3, b + 2) from (a, b), not necessarily (a + 2, b + 3). In fact, the process of generating new pairs branches at each step and the order in which pairs are generated is not determined.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,712
    Thanks
    1642
    Awards
    1

    Re: List the elements of S produced by the first five applications of the recursive d

    Quote Originally Posted by lamentofking View Post
    Let S be the subset of the set of ordered pairs of integers
    defined recursively by Basis step: (0, 0) ∈ S.
    Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S
    and (a + 3, b + 2) ∈ S.
    a) List the elements of S produced by the first five applications of the recursive definition.
    \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}

    I am somewhat confused as to exactly the phrase "the first five applications of the recursive definition" actually means.
    You may need to either drop the (0,0) or make 4 a 5 in the above.

    BTW LaTeX seems to be down: \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Apr 2013
    From
    USA
    Posts
    69
    Thanks
    1

    Re: List the elements of S produced by the first five applications of the recursive d

    Quote Originally Posted by Plato View Post
    \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}

    I am somewhat confused as to exactly the phrase "the first five applications of the recursive definition" actually means.
    You may need to either drop the (0,0) or make 4 a 5 in the above.

    BTW LaTeX seems to be down: \{(0,0)\}\cup\{(3k,2k):k=1,\cdots~4\}
    first five applications are the first five definitions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 13th 2013, 09:12 AM
  2. List five elements in each of the following sets:
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 12th 2013, 07:30 AM
  3. list the elements in set
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 17th 2010, 04:57 PM
  4. list the elements in sets.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 16th 2010, 09:54 AM
  5. List elements of order 10
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: September 8th 2007, 06:38 PM

Search Tags


/mathhelpforum @mathhelpforum