A. Please hand in the following exercises from the text "An Introduction to Analysis, Third
Edition" by William Wade, Prentice Hall, 2004.
10 [ 3, 4 part (8) only]
B. Please hand in the following additional exercises.
Prove in detail using only the Field Axioms: for any a,b,c,d, in R,
(a-b)(c-d)=(ac+bd)-(ad+bc).
Prove that if a field has more than one element, then
1 ≠ 0
is a
consequence of the field axioms and does not have to be assumed as it is in the text's
Postulate 1.