Results 1 to 4 of 4
Like Tree2Thanks
  • 1 Post By Shakarri
  • 1 Post By HallsofIvy

Math Help - zero divides zero...?

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    17

    zero divides zero...?

    I would argue the statement 'zero divides zero' is true.

    We say '3 divides 6' because there exists an integer solution to the eaquation 3k = 6
    experimental evidence suggests there is exactly one solution to the equation ie: k = 2

    Similarly 'zero divides zero' is equivalent to the statement there exists an integer solution to the equation 0k = 0.
    That there are many solutions for k to this equation (rather than exactly one) is not relevant because of the nature of 'there exists'

    My lecturer claims 'zero divides zero' is false because 0 is specifically excluded from the definition of divides.

    What say you?

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2010
    Posts
    17

    Re: zero divides zero...?

    The question in full is to give the answer for X_i when i = 0 for...

    X_i = { x 'element_of' N | x is divisible by i }

    where i is a natural number.

    ...maybe he is arguing 'divides' means something different to 'is divisible by'.

    He is claiming the answer is the empty set but I reckon it should be {0}.

    Whadayathink?
    Last edited by Chad950; January 20th 2014 at 03:20 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    606
    Thanks
    168

    Re: zero divides zero...?

    This video fully explains the reasons why 0/0 is undefined
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,057
    Thanks
    1690

    Re: zero divides zero...?

    Many text books use the term "undefined" for x/0 where x is non-zero and "undetermined" for 0/0.

    I would say that "3 divides 6" because there exist a unique integer, k, such that 6= 3k. More generally, "m divides n if there exist a unique integer k such that n= km". That is not true if m= n= 0.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. p divides (a+b)
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 22nd 2013, 06:23 AM
  2. Replies: 6
    Last Post: October 25th 2012, 05:19 AM
  3. if p divides x then is xy(mod p) = 0 ?
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 11th 2011, 11:52 AM
  4. Replies: 3
    Last Post: October 8th 2011, 04:16 PM
  5. Replies: 2
    Last Post: May 1st 2011, 02:11 PM

Search Tags


/mathhelpforum @mathhelpforum