KnowraWeierstrass functionLinked fromLinked fromThe 10 pages that link to Weierstrass function, each with the reason it gives.All 10Broader topic 4Related 2Compared with 4Continuous functionCompared with: It demonstrates that continuity does not imply smoothness or differentiability.ContinuityBroader topic: It demonstrates that continuity alone does not ensure a tangent or ordinary smoothness.DifferentiabilityBroader topic: It shows that continuity across a whole domain does not guarantee a derivative anywhere.Lipschitz continuityCompared with: Its extreme oscillation contrasts with the regularity imposed by a Lipschitz bound.Karl WeierstrassBroader topic: Its pathological behavior challenged assumptions about how smooth continuous functions must be.Weierstrass approximation theoremCompared with: It illustrates the theorem’s striking reach: even highly irregular continuous functions admit polynomial approximants.Differentiable functionBroader topic: It is a canonical explicit example separating continuity from differentiability.Koch snowflakeRelated: It became a prominent example of the unexpected behavior that motivated such constructions.Hadamard gap theoremRelated: Its classical constructions illustrate how lacunary series can exhibit extreme boundary behavior.Rademacher's theoremCompared with: It shows continuity alone cannot replace the theorem’s Lipschitz condition.