The complex numbers are algebraically closed but they are infinite...
In fact a finite field cannot be algebraically closed. This is easy to see because if F is a finite field and then the polynomial does not have a root in F.
The complex numbers are algebraically closed but they are infinite...
In fact a finite field cannot be algebraically closed. This is easy to see because if F is a finite field and then the polynomial does not have a root in F.
SORRY! I must say prove that all algebraically closed field is infinite.