10183 | An infinite set maps into its own proper subset |

10706 | Dedekind originally thought more in terms of mereology than of sets |

9823 | Numbers are free creations of the human mind, to understand differences |

10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers |

7524 | Order, not quantity, is central to defining numbers |

17611 | We want the essence of continuity, by showing its origin in arithmetic |

10572 | A cut between rational numbers creates and defines an irrational number |

18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut |

17612 | Arithmetic is just the consequence of counting, which is the successor operation |

9824 | In counting we see the human ability to relate, correspond and represent |

9826 | A system S is said to be infinite when it is similar to a proper part of itself |

18087 | If x changes by less and less, it must approach a limit |

13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction |

8924 | Dedekind originated the structuralist conception of mathematics |

9825 | A thing is completely determined by all that can be thought concerning it |

9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position |

9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order |