Prove that {??+?:?,?∈?} is dense in ? if and only if r is an irrational number.

Expert Solution

Colby Messinger answered 1 year ago

Prove that {??+?:?,?∈?} is dense in ? if and only if r is an irrational number.

PROOFS: 1. State the prove The Density Theorem for Rational Numbers 2. Prove that irrational numbers are dense in the set of real numbers

PROOFS: 1. State the prove The Density Theorem for Rational Numbers 2. Prove that irrational numbers are dense in the set of real numbers 3. Prove that rational numbers are countable 4. Prove that real numbers are uncountable 5. Prove that square root of 2 is irrational

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Question

Prove that {??+?:?,?∈?} is dense in ? if and only if r is an irrational number.

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Prove that {??+?:?,?∈?} is dense in ? if and only if r is an irrational number.

Prove that {??+?:?,?∈?} is dense in ? if and only if r is an irrational number.

PROOFS: 1. State the prove The Density Theorem for Rational Numbers 2. Prove that irrational numbers are dense in the set of real numbers

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