Prove the following sequence of theorems. a. An automorphism of a field E carries elements that are
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Prove the following sequence of theorems.
a. An automorphism of a field E carries elements that are squares of elements in E onto elements that are squares of elements of E.
b. An automorphism of the field R of real numbers carries positive numbers onto positive numbers.
c. If σ is an automorphism of R and a < b, where a, b ∈ R, then σ(a) < σ(b).
d. The only automorphism of R is the identity automorphism.
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