# Field Proofs help.

## Main Question or Discussion Point

URGENT Field Proofs help.

I need to prove the following:

1) Prove that if x, y are elements of a field, and X x Y = 0 then either x = 0 or y = 0 .
Write a detailed solution. and mention which of the eld axioms you are using.

2) Let F be a field in which 1 + 1 = 0 . Prove that for any x ∈ F , x = -x

I don't understand how to approach these proofs, since they are so obvious:

1) x times y = 0, of course it will be either x = 0 or y =0, since anything times 0 is 0, but how to go about proving this, I am stuck 2) 1+1=0 => just bring 1 to the right side 1=-1 then for any x=-x. But I don't think this any good of a proof.

I really need some help here, thanks ! ---sdfx . drewd

Mark44
Mentor

I need to prove the following:

1) Prove that if x, y are elements of a field, and X x Y = 0 then either x = 0 or y = 0 .
Write a detailed solution. and mention which of the eld axioms you are using.

2) Let F be a field in which 1 + 1 = 0 . Prove that for any x ∈ F , x = -x

I don't understand how to approach these proofs, since they are so obvious:
You're used to working with a specific field, the real numbers. But here you are working with an arbitrary field.
1) x times y = 0, of course it will be either x = 0 or y =0, since anything times 0 is 0, but how to go about proving this, I am stuck Why is it true that anything times 0 is 0? What field properties are you using?
2) 1+1=0 => just bring 1 to the right side 1=-1 then for any x=-x. But I don't think this any good of a proof.
Right, it's not a good proof. If 1 + 1 = 0, what does that say about 1? For example, in the field of real numbers it is not true that 1 + 1 = 0.
I really need some help here, thanks ! ---sdfx . drewd
You need to be looking at the properties that any field has.

HallsofIvy