Results 1 to 4 of 4

Math Help - Addition on a field with two elements...

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    158

    Addition on a field with two elements...

    Suppose we have a field F = {0, 1}
    1 + 1 = ?

    How does one determine if 1+1 = 1 or if 1+1 = 0?
    Can I define it to be one of the two choices?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by Noxide View Post
    Suppose we have a field F = {0, 1}
    1 + 1 = ?

    How does one determine if 1+1 = 1 or if 1+1 = 0?
    Can I define it to be one of the two choices?

    There's no choice: it must be that 1+1=0 , otherwise we'd get 1=0 ...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    158
    Ah yes, silly of me to ask. Thanks tonio.

    1 + 1 = 1
    1 + [1 + (-1)] = 1 + (-1)
    1 + 0 = 0
    1 = 0
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    Another way of saying the same thing is that every element of a field must have an additive inverse. The additive inverse of 1 cannot be 0 because 1+ 0= 1\ne 0. Since 0 and 1 are the only members of the field, 1 must be its own inverse: 1+ 1= 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Field with three elements
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 1st 2013, 06:54 AM
  2. Quotient ring and field of 9 elements
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: May 22nd 2011, 06:50 AM
  3. Replies: 3
    Last Post: April 27th 2011, 06:57 PM
  4. Elements in a finite field
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 17th 2009, 03:15 AM
  5. The elements of a field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 31st 2008, 03:10 PM

/mathhelpforum @mathhelpforum