Results 1 to 5 of 5

Math Help - quantifiers

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    5

    quantifiers

    Need help with
    Express in quanti ers:
    The sequence {A n}n is element of natural numbers, is strictly decreasing
    Give the negation of as well.
    I am thinking for all N ,there exists x1 < x2, then f(x1) > f(x2) , kinda of lost...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,925
    Thanks
    1764
    Awards
    1

    Re: quantifiers

    Quote Originally Posted by lukeheselden View Post
    Need help with
    Express in quanti ers:
    The sequence {A n}n is element of natural numbers, is strictly decreasing
    Give the negation of as well.
    There are of course several different ways one might do this.
    Here is one. \left( {\forall m \in \mathbb{N}} \right)\left( {\forall n \in \mathbb{N}} \right)\left( {m > n \to x_m  < x_n } \right)

    The negation is, \left( {\exists j \in \mathbb{N}} \right)\left( {\exists k \in \mathbb{N}} \right)\left[ {j > k \wedge x_j  \geqslant x_k } \right]
    Last edited by Plato; August 1st 2011 at 07:33 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2011
    Posts
    27

    Re: quantifiers

    You mixed up the inequalities : the sequence is strictly decreasing ; what you wrote is for a strictly increasing sequence.

    I assume it's a typo, but i point it out for the original poster not to confuse everything.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,925
    Thanks
    1764
    Awards
    1

    Re: quantifiers

    Quote Originally Posted by pece View Post
    You mixed up the inequalities : the sequence is strictly decreasing ; what you wrote is for a strictly increasing sequence.
    Good catch. I misread it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2011
    Posts
    5

    Re: quantifiers

    thanks guys
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quantifiers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 6th 2009, 09:37 PM
  2. Use of Quantifiers
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: October 12th 2009, 10:10 AM
  3. Replies: 1
    Last Post: August 26th 2009, 09:04 AM
  4. Quantifiers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 2nd 2008, 11:11 AM
  5. Quantifiers
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: June 7th 2008, 07:31 PM

Search Tags


/mathhelpforum @mathhelpforum