Results 1 to 2 of 2

Math Help - Abstract Algebra Identity Element question

  1. #1
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Abstract Algebra Identity Element question

    I have to determine whether or not the Reals has an identity element with respect to *, given that x * y = |x - y|.

    To do this, we were taught to solve x * e = x for e.

    So x * e = |x - e| = x, which implies that x - e = x OR x - e = -x.

    Thus e = 0 OR e = 2x.

    Now we want to check that e * x = x * e = x.

    e=0:
    e*x = 0*x = |0-x| = |-x| = x
    x*e = x*0 = |x-0| = x

    e=2x:
    e*x = |2x-x| = x
    x*e = |x -2x| = |-x| = x.

    They both work, but it doesn't make sense that there are two identity elements. What am I missing? Thanks for any help...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,527
    Thanks
    773

    Re: Abstract Algebra Identity Element question

    An identity element must work for all x.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 24th 2012, 03:17 PM
  2. Quick question about identity element
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 28th 2011, 02:20 AM
  3. Replies: 3
    Last Post: March 23rd 2010, 07:05 PM
  4. Abstract Algebra question
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 17th 2010, 05:15 AM
  5. [SOLVED] Abstract algebra semigroup question
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: July 9th 2008, 09:33 PM

Search Tags


/mathhelpforum @mathhelpforum