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The infinitely small is a mathematical quantity and has all its properties in common with the finite A belief in the infinitely small does not triumph easily. Yet when one thinks boldly and freely, the initial distrust will soon mellow into a pleasant certainty ... A majority of educated people will
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admit an infinite in space and time, and not just an "unboundedly large". But they will only with difficulty believe in the infinitely small, despite the fact that the infinitely small has the same right to existence as the infinitely large.
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In a paper of 1875, du Bois-Reymond employed for the first time the method of diagonalization, later associated with the name of
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that converges to a continuous function at every point is the
Fourier series of this function. He is also associated with the
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defines a sufficient condition to guarantee that a function vanishes almost everywhere.
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Orders of
Infinity: The 'Infinitärcalcül' of Paul Du Bois-Reymond
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Kassel 1854, dort werden aber einschränkendere
Annahmen gemacht.
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Teubner 1909, S. 26. Nach Bolza stammt der älteste Beweis von
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Erläuterungen zu den
AnfangsgrĂĽnden der Variationsrechnung.
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of which he proved a refined version based on that of
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96:. Du Bois-Reymond also established that a
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225:Vorlesungen ĂĽber Variationsrechnung.
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319:. You can help Knowledge by
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69:. His interests included
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