Originally Posted by

**AlexP** I got it. Since we're in characteristic 2 we have $\displaystyle f(a)=f(a+1)$ for arbitrary $\displaystyle a$ (I did work out the details).

Question about something I'm not clear on though... My book (Contemporary Abstract Algebra, Gallian, 5th ed.) says "A field $\displaystyle E$ is an extension field of a field $\displaystyle F$ if $\displaystyle F \subseteq E$ and the operations of $\displaystyle F$ are those of $\displaystyle E$ restricted to $\displaystyle F$." That wording bothers me... Is that saying that E inherits the operations of F (and thus has the same characteristic?)? That's not what it seems to be saying to me, but it's what seems to make sense.