Timeline for Consequences of lack of rigour
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2020 at 22:27 | comment | added | santker heboln | The existence of pathological objects may also indicate that the definitions are somehow lacking and should be corrected or broadened in scope. That is why convenient categories are being studied and why things like tame topology are being considered. The fact is that mathematical structures are never fixed, but in constant flux. They reflect our current level of insight, which is rather shallow. | |
| Feb 28, 2019 at 17:24 | comment | added | Wrzlprmft | @PyRulez: Our number system is the prime example – Well, but then you can describe reality just fine with rational numbers. It may just get a bit tedious. Still, I can phrase that better; see my edit. | |
| Feb 28, 2019 at 17:23 | history | edited | Wrzlprmft | CC BY-SA 4.0 |
added 26 characters in body
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| Feb 28, 2019 at 12:32 | comment | added | Christopher King | "Since mathematicians are usually good of thinking about relevant cases, this means that the cases in which such a statement fails are few in number as compared to those where it holds." It is actually more typical that the statement failing is the norm (if it does fail), and that the set of "well-behaved" cases is small in some sense, if not in cardinality. Our number system is the prime example: irrational, transcendental, incomputable, arithmetically undefinable, imaginary. "Most" functions and topologies are also pathological. Exceptional objects are exceptional for a reason. | |
| S Feb 28, 2019 at 11:45 | history | answered | Wrzlprmft | CC BY-SA 4.0 | |
| S Feb 28, 2019 at 11:45 | history | made wiki | Post Made Community Wiki by Wrzlprmft |