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Class Contents

• Convergence of power series
• A nowhere differentiable function

We can also use this to reprove the differentiability of power series.

Proof.

Now we can use the results with uniform convergence to construct some interesting functions:

1. a nowhere differentiable function
2. a space-filling curve

Proof.

A nowhere differentiable function

But, one of the following holds:

Space-filling Curves