Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Plato

Thread: Provide a convincing arguement

  1. #1
    Newbie
    Joined
    Mar 2017
    From
    Ireland
    Posts
    2

    Provide a convincing arguement

    Provide a convincing argument that if a ϵ R then there is positive integer, n, such that n>a.

    My attempt:

    If n=a+x where x
    ϵ R > 0 then n>a for any n>0.

    Really unsure though.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,092
    Thanks
    2569
    Awards
    1

    Re: Provide a convincing arguement

    Quote Originally Posted by Fergal View Post
    Provide a convincing argument that if a[FONT=arial] ϵ R then there is positive integer, n, such that n>a.
    As with all mathematics, you must have a list of axioms. We do not have your list.
    The completeness axiom states that: Any non-empty set that is bounded above has a least upper bound.
    If the statement is false then $a$ is an upper bound for $\mathbb{Z}^+$
    So use the axiom and let $k$ be the LUB of $\mathbb{Z}^+$.
    Now $k-1<k$ so it is not an upper bound, by the meaning of least.
    Thus $\exists j\in\mathbb{Z}^+: k-1<j\le k$.
    But that means $k+1<j+1\in\mathbb{Z}^+$
    Do you see a contradiction?
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2017
    From
    Ireland
    Posts
    2

    Re: Provide a convincing arguement

    That pointed me in right direction. Appreciate it Plato :-)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Please solve my maths arguement!
    Posted in the New Users Forum
    Replies: 2
    Last Post: Dec 18th 2012, 03:09 AM
  2. What's wrong with the arguement
    Posted in the Calculus Forum
    Replies: 15
    Last Post: Apr 24th 2008, 07:47 PM
  3. Cominatorial arguement as a proof
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Apr 18th 2008, 07:48 PM
  4. valid arguement?
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Oct 15th 2007, 06:35 PM

/mathhelpforum @mathhelpforum