Results 1 to 3 of 3

Math Help - proof involving natural numbers

  1. #1
    Super Member
    Joined
    Feb 2008
    Posts
    535

    proof involving natural numbers

    How do I prove that N+ (positive natural numbers) are closed under multiplication?

    Any advice...Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by jzellt View Post
    How do I prove that N+ (positive natural numbers) are closed under multiplication?

    Any advice...Thanks in advance.
    see here. what you want is on the last page. but the proof refers to things on previous pages.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by jzellt View Post
    How do I prove that N+ (positive natural numbers) are closed under multiplication?

    Any advice...Thanks in advance.
    We know there is a unique function \cdot : \mathbb{N}\times \mathbb{N}\to \mathbb{N} such that \cdot (n,0) = 0\text{ and }\cdot(n,m+1) = \cdot(n,m) + m for all n,m\in \mathbb{N}. We will write n\cdot m instead of \cdot (n,m). Now we want to prove that if a,b\in \mathbb{N}^+ then a\cdot b\in \mathbb{N}^+. Well, here is a hint, if a>0 then a=a_0+1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multiplication of Natural Numbers proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 17th 2011, 03:32 PM
  2. Proof of m > n in the Natural Numbers
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: February 17th 2011, 10:32 AM
  3. Proof that 1 is in the Natural Numbers
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: February 16th 2011, 12:12 PM
  4. [SOLVED] Inequality proof involving natural numbers.
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 13th 2009, 09:19 AM
  5. [SOLVED] Proof involving natural numbers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 12th 2009, 10:20 PM

Search Tags


/mathhelpforum @mathhelpforum