weierstrassian love

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from The Century Dictionary and Cyclopedia

  • Of or pertaining to, or named from, K. T. W. Weierstrass, a German mathematician (born 1816).
  • The function
  • In certain cases, as when p = 1, b ⟨ 1, ab ⟩ 1 + , this fuuction, although continuous, has no differential coefficient. In fact, the curve of the function, when seen at a distance, appears like a simple curve of sines; but when it is magnified, small waves are seen upon it; under a higher magnifying power, wavelets on these waves; and so on ad infinitum; so that, although f (x + h) − fx becomes infinitesimal with h, yet it has no limiting ratio to h.


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