Abstract
Set theory is concerned with those mathematically defined infinite totalities or domains which are called “sets” and among which the “finite” ones only occur as a special borderline case. Since an infinite totality can never be given or presented empirically, the definition of such a domain can always only proceed axiomatically through the specification of a system of conditions that this ideally posited infinite domain, which only exists as an idea in Plato’s sense, is supposed to satisfy. Examples of such axiomatically defined infinite totalities or sets are the system of the natural numbers in the sense of Peano’s postulates and the system of the reals in the sense of Hilbert’s axioms.
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© 2010 Springer-Verlag Berlin Heidelberg
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(2010). Zermelo s1932d. In: Ebbinghaus, HD., Fraser, C., Kanamori, A. (eds) Ernst Zermelo - Collected Works/Gesammelte Werke. Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79384-7_32
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DOI: https://doi.org/10.1007/978-3-540-79384-7_32
Publisher Name: Springer, Berlin, Heidelberg
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