Mathematics · Real Analysis
Let Thomae's function h(x) be defined on the interval [0, 1] by h(x) = 1 if x = 0; h(x) = 1/q if x is rational and x = p/q in lowest terms (q > 0); and h(x) = 0 if x is irrational. Then which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1h(x) is continuous everywhere on [0, 1].
- 2h(x) is discontinuous only at irrational points.
- 3h(x) is Riemann Integrable.✓
- 4h(x) is unbounded.
Correct answer
h(x) is Riemann Integrable.
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