Timeline for What notions are used but not clearly defined in modern mathematics?
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8 events
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| Nov 12 at 1:39 | comment | added | C7X | I would argue that the natural numbers are rigorously defined (in relevance to the Emerton quote) because for any usually accepted foundation of mathematics (e.g. ZFC), there is a formula in its language that is true of some object iff it is a natural number. While the set of natural numbers may differ between models of ZFC, so will the sets of most other commonly used objects in mathematics (e.g. the set of finite fields), while I think most would argue that there is a rigorous definition of what it means for a set to be a finite field. | |
| Aug 23, 2018 at 0:36 | comment | added | David Roberts♦ | @Gerry as countable sets with a (well-founded) linear order with successor the N with 0 and the N with no 0 are uniquely isomorphic, so unless you need the additive monoid of natural numbers, rather than the additive semigroup, then it won't make too much difference. | |
| Aug 23, 2018 at 0:26 | history | edited | none | CC BY-SA 4.0 |
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| Aug 22, 2018 at 22:34 | comment | added | Gerry Myerson | There isn't even any universal agreement as to whether zero is in $\bf N$. | |
| Aug 22, 2018 at 18:11 | history | edited | none | CC BY-SA 4.0 |
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| Aug 22, 2018 at 17:50 | review | Late answers | |||
| Aug 22, 2018 at 18:00 | |||||
| S Aug 22, 2018 at 17:34 | history | answered | none | CC BY-SA 4.0 | |
| S Aug 22, 2018 at 17:34 | history | made wiki | Post Made Community Wiki by none |