Prove the theorem, Prove the following theorem: If x y +

Prove the theorem

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Reference no: EM13136688

1. Using the axioms of real numbers prove the following theorem:
8x; y 2 R (x < y) ) (y < x) _ (y = x)

(Note: This is the theorem that allows us to replace x 6 < y with x y.)
2. Let x; y 2 R and 2 R
+
. Prove the following theorem:
If x y + for any > 0 then x y.
For this proof you may assume any theorems stated in lectures.
Hint: Write the theorem as a conditional logic statement (using any necessary quanti er(s))
and then consider an indirect proof.
1

Reference no: EM13136688

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