In each of the following exercises, verify the given statement carefully, proceeding step by step. Validate each step that involves an inequality by using some statement found in this section.
a) Interpreting a rational m/n as m · n−1 ∈ R, use Postulate 1 to prove that
for m, n, p, q, l ∈ Z and n, q, l ≠ 0.
b) Using Remark 1.1, Prove that Postulate 1 holds with Q in place of R.
c) Prove that the sum of a rational and an irrational is always irrational. What can you say about the product of a rational and an irrational?
d) Let m/n, p/q ∈ R with n, q > 0. Prove that
(Restricting this observation to Q gives a definition of “<” on Q.)
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.