Question 1. Let F be an ordered ﬁeld. For each of the following statements, prove the...

Question 1. Let F be an ordered ﬁeld. For each of the following statements, prove the statement or provide a counterexample.
(a) For all x,y,z,w ∈F, if x < y and xw < yz, then w < z.

(b) If x,y,z,w ∈F, then |x + w|≤|x + y|+|y + z|+|z + w|

Let x ∈R, a ∈R, and b ∈R.
(a) Suppose that |x−a| = 3|x−b|. Let

c =(9b−a)/ 8
. Prove that |x−c| = 3 8|a−b|

Expert Solution

Colby Messinger answered 2 years ago

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