1880 | works |
p.3 | 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity |
p.7 | 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory |
p.11 | 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties |
p.14 | 10082 | There are infinite sets that are not enumerable |
p.19 | 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets |
p.27 | 8631 | Cantor says that maths originates only by abstraction from objects |
p.29 | 13465 | Only God is absolutely infinite |
p.29 | 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity |
p.38 | 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals |
p.40 | 9971 | Cantor introduced the distinction between cardinals and ordinals |
p.42 | 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line |
p.43 | 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between |
p.48 | 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers |
p.51 | 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' |
p.60 | 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it |
p.99 | 10112 | The naturals won't map onto the reals, so there are different sizes of infinity |
p.163 | 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 |
p.293 | 9892 | Cantor showed that ordinals are more basic than cardinals |
p.304 | 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order |
p.484 | 13016 | The Axiom of Union dates from 1899, and seems fairly obvious |
I.1 | p.21 | 18176 | Pure mathematics is pure set theory |
1883 | Grundlagen (Foundations of Theory of Manifolds) |
p.52 | 15911 | Ordinals are generated by endless succession, followed by a limit ordinal |
p.247 | 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation |
1885 | Review of Frege's 'Grundlagen' |
1932:440 | p.60 | 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate |
1897 | The Theory of Transfinite Numbers |
p.4 | 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections |
p.85 | p.22 | 9616 | A set is a collection into a whole of distinct objects of our intuition or thought |
1899 | Later Letters to Dedekind |
p.366 | 17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another |
1915 | Beitrage |
§1 | p.599 | 9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order |