October 11th, 2018, 01:19 PM |
#11 | |

Senior Member Joined: Jun 2014 From: USA Posts: 422 Thanks: 26 | Quote:
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October 12th, 2018, 03:31 AM |
#12 | |

Senior Member Joined: Jun 2014 From: USA Posts: 422 Thanks: 26 | Quote:
Cantor made use of "in / not in" operations to construct his self-referential argument whereas I made use of "subset / not subset" operations to construct mine. If I had made $G$ larger so as to contain the set $H$ for any possible function $r$, then the cardinality of $G$ would be greater than the cardinality of $D$. Cantor's proof that no set can be surjected onto its powerset was obviously much more eloquent, but this is another way of showing the difference in cardinality between two sets. So, if anyone doesn't like Cantor's arguments (it seems we have a few running around this forum), maybe they could accept my argument as constructed with a suitable $G$. | |

October 12th, 2018, 04:42 AM |
#13 | |

Senior Member Joined: Aug 2017 From: United Kingdom Posts: 284 Thanks: 86 Math Focus: Algebraic Number Theory, Arithmetic Geometry | Quote:
This is one reason that learning to write proofs and establishing rigour early on in your mathematical education is important: it gives you the ability to challenge any potentially flawed intuitions before they root themselves too deeply in your mind. | |