Definition:Set/Historical Note

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Historical Note on Set

The concept of a set first appears in Bernhard Bolzano's posthumous ($1851$) work Paradoxien des Unendlichen (The Paradoxes of the Infinite).

The first investigation into the concept in any depth was made by Georg Cantor in his two papers called Beiträge zur Begründung der transfiniten Mengenlehre ($1895$ and $1897$).

It was Georg Cantor who defined a set as being:

a Many that allows itself to be thought of as a One.
-- Georg Cantor, A. Fraenkel and E. Zermelo, Gesammelte Abhandlungen (Berlin: Springer-Verlag, $1932$)

This definition was directly inspired by a problem raised by Bernhard Riemann in his paper Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe of $1854$, on the subject of Fourier series.