Results 1 to 2 of 2

Math Help - Prove equal powers (probably fairly primitive)

  1. #1
    Member Pranas's Avatar
    Joined
    Oct 2010
    From
    Europe. Lithuania.
    Posts
    81

    Prove equal powers (probably fairly primitive)

    Hello.

    My discrete mathematics course has just started, so I'm not very good even at probably fairly easy things:

    Prove if \displaystyle \[G = A \times B\] is a bijection between finite sets \displaystyle \[A\] and \displaystyle \[B\] then \displaystyle \[\left| A \right| = \left| B \right|\].

    It looks pretty obvious because of the nature of this bijection, but I just can't seem to figure out notations to prove it in a mathematical way.

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,530
    Thanks
    774
    A bijection is a function, but if A is nonempty and |B| > 1, then A x B is not a function. If there is no mistake in the question, then the fact that A x B is a bijection implies that |A| = |B| = 1 or |A| = |B| = 0, so |A| = |B|.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equal Sums of Like Powers
    Posted in the Math Forum
    Replies: 5
    Last Post: May 29th 2010, 02:55 AM
  2. Prove that 2 is a primitive root modulo p.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 21st 2010, 05:51 PM
  3. Prove Primitive over Z_5
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 6th 2008, 12:44 PM
  4. prove H_T less than or equal to S_n
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 16th 2008, 02:59 PM
  5. powers modulo p and primitive root question
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: June 16th 2008, 10:57 AM

Search Tags


/mathhelpforum @mathhelpforum