Interactive Real Analysis

• Real Analysis
• 1. Sets and Relations
• 1.1. Notation and Set Theory
• 1.2. Relations and Functions
• 1.3. Equivalence Relations and Classes
• 1.4. Natural Numbers, Integers, and Rational Numbers
• 2. Infinity and Induction
• 3. Sequences of Numbers
• 4. Series of Numbers
• 5. Topology
• 6. Limits, Continuity, and Differentiation
• 7. The Integral
• 8. Sequences of Functions
• 9. Historical Tidbits
• Java Tools

1.4. Natural Numbers, Integers, and Rational Numbers

Example 1.4.6: n-th Root is not Rational

Prove that if p is a prime number, then p^1/n, where n > 1, is not rational.

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Proofs that show that something is not the case call out for proofs by contradiction. Thus, you might want to start out a possible proof as follows:

Assume p^1/n is rational, i.e. p^1/n = ^a/_b

If this would result in a contradiction (perhaps to the fact that p is assumed to be a prime number), we would have a classical proof by contradiction.

Soooo ... any thoughts?