15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory |

15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation |

9616 | A set is a collection into a whole of distinct objects of our intuition or thought |

10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity |

17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another |

13016 | The Axiom of Union dates from 1899, and seems fairly obvious |

10082 | There are infinite sets that are not enumerable |

13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it |

15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' |

15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line |

9971 | Cantor introduced the distinction between cardinals and ordinals |

15911 | Ordinals are generated by endless succession, followed by a limit ordinal |

9892 | Cantor showed that ordinals are more basic than cardinals |

14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order |

11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 |

15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between |

15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals |

15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties |

15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers |

13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity |

10112 | The naturals won't map onto the reals, so there are different sizes of infinity |

15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections |

9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate |

18176 | Pure mathematics is pure set theory |

8631 | Cantor says that maths originates only by abstraction from objects |

13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets |

9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order |

13465 | Only God is absolutely infinite |