1) can anyone explain me about characteristic of fields? is in 1+1+1+1+1

+ defined as the addition operator of F? what about a*n when a belongs to F and n is char F.i know it eqauls 0 by making that a=a*1 and n*1 is 0 but is the * the multiplying operator of F because n doesn't have to belong to F.

2)Let F be a field of characteristic p (prime number). prove that Zp is contained in F. Zp={0,1,.....,p-1} regarding modulo p.

i know that 1 belongs to F as weel as 0. but is 1+1=2 in F ?

Thank You Guys.