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 Beitr√§ge zur Begr√ľndung der transfiniten Mengenlehre ($1895$ and $1897$).

It was Georg Cantor who, in $1874$, defined a set thus:

By a set $M$ we understand any collection into a whole of definite and separate objects $m$ of our intuition or our thought.

Hence the definition of a set as:

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.


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