1. Let α < β be real numbers and N ∈ N. (a). Show that if...

1. Let α < β be real numbers and N ∈ N.

(a). Show that if β − α > N then there are at least N distinct integers strictly between β and α.
(b). Show that if β > α are real numbers then there is a rational number q ∈ Q such β > q > α.

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2. Let x, y, z be real numbers.The absolute value of x is defined by

|x|= x, if x ≥ 0 ,

−x, if x < 0

Define the following statements. Assume that the product of two positive real numbers is positive.

(a). Show that |x−y| = |y−x|.

(b). Show that if z<0 and x ≤ y, then zy ≤ zx.

(c). Show that |x+y| ≤ |x|+|y|.

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Answer both questions plz. Will rate.

Expert Solution

Colby Messinger answered 2 years ago

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