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Abstract Algebra Groups

  1. Jul 20, 2011 #1
    The .pdf can be ignored.

    Let A + B = (A - B) U (B - A) also known as the symmetric difference.

    1. Look for the identity and let e be the identity element

    A + e = A
    (A - e) U (e - A) = A

    Now there are two cases:

    1. (A - e) = A
    This equation can be interpreted as removing from A all elements that belong to e to yield the set A. In order for this statement to be true, the identity element e must be the empty set.

    2. (e - A) = A
    This equation can be interpreted as removing from e all elements that belong to A to generate a set A. Is this statement undefined?
     

    Attached Files:

    Last edited: Jul 20, 2011
  2. jcsd
  3. Jul 20, 2011 #2
    If A=A'(inverse) then why does A+A'={}(empty set)?
     
  4. Jul 20, 2011 #3
    A + A' is the symmetric difference, and not by means of normal addition.
     
  5. Jul 20, 2011 #4
    Ah. Well I learned something :)
     
  6. Jul 21, 2011 #5
    (e-A) must equal something else and not A. Moreover it must equal something such that the union of (A-e)=A with (e-A)=X is A U X=A. Im sure you are aware of such a set =).

    It cant be undefined or else were breaking the conditions of what it is to be a group. A and e are elements of the group so (A-e)U(e-A) must be too. right?
     
    Last edited: Jul 21, 2011
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