Weierstrass's Non-Differentiable Function¶
Hardy. (1916). Weierstrass's Non-Differentiable Function. Transactions of the American Mathematical Society.
Cited by¶
1 citation across 1 artifact.
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Domain-specific¶
- Derivative
- Differentiability is strictly stronger than continuity: every differentiable function is continuous, but continuous functions can fail to be differentiable (the absolute value function at zero, or, more dramatically, the Weierstrass function, which is continuous everywhere and differentiable nowhere
This sourceRigorous treatment of the Weierstrass function as everywhere continuous and nowhere differentiable, for the general parameter range.
- Differentiability is strictly stronger than continuity: every differentiable function is continuous, but continuous functions can fail to be differentiable (the absolute value function at zero, or, more dramatically, the Weierstrass function, which is continuous everywhere and differentiable nowhere
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