Timeline for Conditions equivalent to finiteness
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| Feb 13, 2021 at 14:37 | answer | added | Tim Campion | timeline score: 3 | |
| Feb 13, 2021 at 14:05 | comment | added | Alec Rhea | @TimCampion Most certainly, let one thousand flowers bloom. I just saw an opportunity to nitpick and had to take it ;). | |
| Feb 13, 2021 at 14:01 | comment | added | Tim Campion | ... a "set" really is nothing more than an object of the category of sets; the axioms tell us something about what this sort of "set" is in just the same way that the axioms of ZFC tell us something about what its sort of "set" is. In Mike Shulman's terminology, there are "material set" theories like ZFC and "structural set" theories like ETCS. Both are adequate to support most of the ways that sets are used outside of pure set theory, so it's not unreasonable for mathematicians to differ on which sort of "set" is the default meaning for them. | |
| Feb 13, 2021 at 14:01 | comment | added | Tim Campion | @AlecRhea That's fair. I'm reminded of the discussion in the comments here the other day, although that was over a slightly different question -- I agree that although ZFC doesn't "define" what a set is, the rules it gives for reasoning about them "say something" about about what a set is. Note, though, that in some foundational approaches, e.g. in ETCS-based approaches,... | |
| Feb 13, 2021 at 13:49 | comment | added | Alec Rhea | @TimCampion I’m interested in any notion that matches our intuition of the finite. I do have a philosophical nitpick with the phrasing of your question; I don’t view sets as ‘the objects of the category of sets’ because the definition of that category doesn’t actually tell me anything about what a set is, at least not in the sense that the axioms of some set theory would. Indeed, ‘the category of sets’ changes depending on what set theoretical axioms are in the universe — in NF, for example, the category of sets is not Cartesian closed. | |
| Feb 13, 2021 at 12:58 | comment | added | Tim Campion | I think you're talking about finiteness of sets. Are you also interested in finiteness in other categories? | |
| Jan 19, 2021 at 10:42 | answer | added | Hanul Jeon | timeline score: 5 | |
| Jan 18, 2021 at 19:19 | answer | added | Asaf Karagila♦ | timeline score: 5 | |
| Jan 18, 2021 at 19:13 | history | edited | gmvh |
Added top-level tags
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| Jan 18, 2021 at 16:34 | history | became hot network question | |||
| Jan 18, 2021 at 13:56 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jan 18, 2021 at 10:16 | history | edited | Alec Rhea | CC BY-SA 4.0 |
fixed error pointed out by abx
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| Jan 18, 2021 at 10:16 | comment | added | Alec Rhea | @abx Total brain fart, thanks for the catch. | |
| Jan 18, 2021 at 9:43 | comment | added | abx | If we have the same definition for the characteristic of a field, 2. is definititely false. | |
| Jan 18, 2021 at 9:32 | answer | added | YCor | timeline score: 5 | |
| Jan 18, 2021 at 9:19 | answer | added | Qiaochu Yuan | timeline score: 4 | |
| Jan 18, 2021 at 9:16 | answer | added | YCor | timeline score: 5 | |
| Jan 18, 2021 at 9:13 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Jan 18, 2021 at 8:41 | history | edited | Alec Rhea | CC BY-SA 4.0 |
added 10 characters in body
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| Jan 18, 2021 at 8:41 | comment | added | Alec Rhea | @NoahSchweber Thank you for the correction. | |
| Jan 18, 2021 at 8:41 | comment | added | Noah Schweber | 4 should say "countably infinite subsets" - trivially, a set is finite iff it has no infinite subsets. | |
| Jan 18, 2021 at 8:39 | history | edited | Alec Rhea | CC BY-SA 4.0 |
added 5 characters in body
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| Jan 18, 2021 at 8:34 | history | asked | Alec Rhea | CC BY-SA 4.0 |