Interactive Real Analysis

• Real Analysis
• 1. Sets and Relations
• 2. Infinity and Induction
• 3. Sequences of Numbers
• 4. Series of Numbers
• 5. Topology
• 6. Limits, Continuity, and Differentiation
• 7. The Integral
• 8. Sequences of Functions
• 8.1. Pointwise Convergence
• 8.2. Uniform Convergence
• 8.3. Series and Power Series
• 8.4. Taylor Series
• 8.5. Approximation Theory
• 9. Historical Tidbits
• Java Tools

8.2. Uniform Convergence

Example 8.2.2 (e): Uniform Convergence on R

Can you find a uniformly convergent sequence for all real numbers?

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We saw an example of a sequence f_n(x) = x/n that converges uniformly on any compact subset of R but fails to converge on all of R. Our other examples were all defined on bounded intervals, so finding a uniformly convergent sequence for all real numbers is a valid question.

Well, then ... go for it!