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Math Help - Simple Field Question.

  1. #1
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    Simple Field Question.

    Suppose that K is a field containing an element c such that c≠0 and c+c=0. Show that 1+1=0 in this field.
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  2. #2
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    Well, what have you tried so far?
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  3. #3
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    im thinking c1+c1=0
    then c(1+1)=0
    but then i get c=0 which cant happen..
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  4. #4
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    Quote Originally Posted by calculuskid1 View Post
    im thinking c1+c1=0
    then c(1+1)=0
    but then i get c=0 which cant happen..
    You got that because you divided by 0...

    Hint: all non-zero elements of a field have a ________ inverse.
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  5. #5
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    im guessing multiplicable inverse?
    so:
    (1/c)c(1+1)=0(1/c) Then
    1+1=0?
    is that correct?
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  6. #6
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by calculuskid1 View Post
    im guessing multiplicable inverse?
    so:
    (1/c)c(1+1)=0(1/c) Then
    1+1=0?
    is that correct?
    Yep, an alternative way of writing it is

    c+c=0

    \implies c^{-1}(c+c)=c^{-1}\cdot0

    \implies c^{-1}\cdot c+c^{-1}\cdot c=0

    \implies 1+1=0
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