1.Previous
3.Next

and the multiplicative identity ; the sum of a finite number of must be fixed, as well as the additive inverses of these sums (that is, the automorphism fixes all integers); finally, since every rational number is the quotient of two integers, all rational numbers must be fixed by any automorphism.
**The field of the real numbers has no automorphisms other than the identity. Indeed, the rational numbers must be fixed

1.Previous
3.Next