Interactive Real Analysis
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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
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Proposition 8.1.5: Supremum Norm and Uniform Convergence
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A sequence
f
_{n}
:
D
R
converges uniformly to
f:
D
R
if and only if
f
_{n}
 f
_{D}
= 0
Context
The proof follows immediately from the definitions.
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