Let x, y ∈ [0, 1] be such that x ≠ y. Which of the following statements is true for every ε > 0?

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Mathematics · Real Analysis

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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There exists a positive integer N such that |x - y| < 2n ε for every integer n ≥ N.

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Answer 1

There exists a positive integer N such that |x - y| < 2n ε for every integer n ≥ N.

Answer 2

There exists a positive integer N such that 2n ε < |x - y| for every integer n ≥ N.

Answer 3

There exists a positive integer N such that |x - y| < 2-n ε for every integer n ≥ N.

Answer 4

For every positive integer N, |x - y| < 2-n ε for some integer n ≥ N.

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