Mathematics · Real Analysis
Let S be a subset of the open interval (0, 1) consisting of all real numbers α = 0.a1a2a3... whose infinite decimal expansion satisfies ai ∈ {0, 2, 4} for all i ≥ 1. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There is a bijective map from &mathbb;N to S.
- 2There is a surjective map from S onto (0, 1).✓
- 3There is a bijective map from &mathbb;N to (0, 1) \ S.
- 4S is a countable set and (0, 1) \ S is uncountable.
Correct answer
There is a surjective map from S onto (0, 1).
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