Mathematics · Real Analysis
Suppose f: ℝ → ℝ is the greatest integer function defined as f(x) = n for n ≤ x < n + 1, where n is any integer. Which of the following statements is correct regarding f on the entire real line ℝ?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f is not Riemann integrable on ℝ because Riemann integration is defined only on bounded intervals.✓
- 2f is bounded on ℝ.
- 3f is uniformly continuous on ℝ.
- 4f is Riemann integrable on ℝ.
Correct answer
f is not Riemann integrable on ℝ because Riemann integration is defined only on bounded intervals.
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