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4. (a) Use the Method of Smallest Counterexamples based on the Well-Ordering Prin- ciple to prove the following: For all n E N, n! ≤n". (b) Let a and b be nonzero integers. Use the Well-Ordering Principle to show that there is a smallest positive linear combination of a and b.

4. (a) Use the Method of Smallest Counterexamples based on the Well-Ordering Prin- ciple to prove the following: For all n E N, n! ≤n". (b) Let a and b be nonzero integers. Use the Well-Ordering Principle to show that there is a smallest positive linear combination of a and b.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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4. (a) Use the Method of Smallest Counterexamples based on the Well-Ordering Prin- ciple to prove the following: For all n E N, n! ≤n". (b) Let a and b be nonzero integers. Use the Well-Ordering Principle to show that there is a smallest positive linear combination of a and b.
Transcribed Image Text:4. (a) Use the Method of Smallest Counterexamples based on the Well-Ordering Prin- ciple to prove the following: For all n E N, n! ≤n". (b) Let a and b be nonzero integers. Use the Well-Ordering Principle to show that there is a smallest positive linear combination of a and b.
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