# Math Help - Simple Field Question.

1. ## 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.

2. Well, what have you tried so far?

3. im thinking c1+c1=0
then c(1+1)=0
but then i get c=0 which cant happen..

4. Originally Posted by calculuskid1
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.

5. im guessing multiplicable inverse?
so:
(1/c)c(1+1)=0(1/c) Then
1+1=0?
is that correct?

6. Originally Posted by calculuskid1
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

$c+c=0$

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

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

$\implies 1+1=0$