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A set is a Many that allows itself to be thought of as a One.
Georg Cantor
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The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.
Georg Cantor
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Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.
Georg Cantor
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In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.
Georg Cantor
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Myth is neither a lie nor a confession: it is an inflexion.
Roland Barthes
Georg Cantor
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Born:
March 3, 1845
Died:
January 6, 1918
(aged 72)
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