Timeline for Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?
Current License: CC BY-SA 4.0
12 events
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| May 6 at 17:41 | comment | added | Mauro ALLEGRANZA | @Anixx - there were two ways of comparing collections: either checking that one is a proper sub-collection of the other or counting the respective elements. For finite collections the two criteria produce the same result; not so for infinite ones. Cantor choose the counting criteria | |
| May 6 at 16:43 | comment | added | Anixx | You are saying as if Euclid's principle was unapplicable to infinite sets. | |
| S May 2, 2022 at 11:35 | history | suggested | CommunityBot | CC BY-SA 4.0 |
fixed broken link to projecteuclid.org
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| May 1, 2022 at 15:06 | review | Suggested edits | |||
| S May 2, 2022 at 11:35 | |||||
| Jun 17, 2020 at 8:34 | history | edited | CommunityBot |
Commonmark migration
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| Jan 17, 2019 at 7:09 | history | edited | Mauro ALLEGRANZA | CC BY-SA 4.0 |
deleted 8 characters in body
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| Jan 16, 2019 at 21:21 | comment | added | rus9384 | @Not_Here So, you will argue that according to modern math they are not both aleph_0? That aleph_0 = aleph_0 is trivial. But my question is where does the one-to-one correspondence implies the same number of elements. In your intuition? Maybe. But not in mine. | |
| Jan 16, 2019 at 14:54 | comment | added | Not_Here | @rus9384 Nobody said that they're "equal", is that really your best attempt? Just because two objects share one property (in this case having the same cardinality) that makes them equal simpliciter? Nobody with even a cursory understanding of mathematics thinks that. | |
| Jan 16, 2019 at 14:23 | comment | added | rus9384 | @Not_Here Well, I don't know why would two infinities be equal in set theory if they are not in analysis. Seems inconsistent. | |
| Jan 16, 2019 at 10:57 | comment | added | Not_Here | @rus9384 Your comment doesn't make sense. It's like saying that an infinite series doesn't converge because if you take an initial finite segment and sum it you don't get the value the entire infinite series converges to. If you're a finitist then okay, but if you agree that infinity makes sense then what you're saying doesn't make any sense. If you're a finitist but you don't announce that when you argue with someone who does accept infinity, you come off as if you're arguing in bad faith and not being up front about what is actually going on. | |
| Jan 16, 2019 at 9:31 | comment | added | rus9384 | Why would Galileo's paradox be a paradox though? Inifinity is inapproachable and set of squares will be much smaller than set of natural numbers if their largest element is the same (and greater than 1). | |
| Jan 16, 2019 at 7:21 | history | answered | Mauro ALLEGRANZA | CC BY-SA 4.0 |