Ideas from 'Grundlagen (Foundations of Theory of Manifolds)' by George Cantor [1883], by Theme Structure

[found in 'From Kant to Hilbert: sourcebook Vol. 2' (ed/tr Ewald,William) [OUP 1996,0-19-850536-1]].

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4. Formal Logic / F. Set Theory ST / 1. Set Theory

15946

Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation

			Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞.....
			From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers

15911

Ordinals are generated by endless succession, followed by a limit ordinal

			Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence).
			From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4