# Thread: definition of a subfield

1. ## definition of a subfield

in the definition of a subfield we have that it contains both the 0 and 1 elements.

prove- this condition can be replaced by "it has at least 2 elements"

I'm quite confused as to how to start this, if someone could give me a hint to get started that would be great.

thanks for any help

2. ## Re: definition of a subfield

Originally Posted by hmmmm
in the definition of a subfield we have that it contains both the 0 and 1 elements.

prove- this condition can be replaced by "it has at least 2 elements"

I'm quite confused as to how to start this, if someone could give me a hint to get started that would be great.

thanks for any help
Well, in a field you assume that $1\ne 0$ and since every field has a multiplicative and additive identity.....