Timeline for mixing theorem with definition (definition with proof)
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2018 at 20:45 | answer | added | Nik Weaver | timeline score: 2 | |
| Oct 19, 2018 at 9:10 | comment | added | Emanuele Paolini | My impression is that the notation $(-)^\times$ was invented by purpose to differentiate from $(-)^*$. This makes sense because $*$ has nothing to do with multiplication (outside programming languages). | |
| Oct 19, 2018 at 7:53 | comment | added | Najib Idrissi | @LSpice And yet the notation $(-)^*$ to exclude zero is widely understood. The IOS didn't invent a standard out of thin air... | |
| Oct 19, 2018 at 4:19 | answer | added | Francois Ziegler | timeline score: 4 | |
| Oct 19, 2018 at 2:25 | comment | added | LSpice | @KeithKearnes, I find it hard to believe that any organisation can successfully change mathematicians' habits (and I imagine that the prescription that $\mathbb N$ contains $0$, though I agree with it, has plenty of disputants, its standardisation not withstanding); but, anyway, in light of that information it would be perfectly fine to take my position as agitating either against the IOS's useage, or, perhaps more amicably, for a change in the standard. | |
| Oct 19, 2018 at 1:52 | comment | added | Keith Kearnes | @LSpice: The international Organization for Standardization has stipulated that the number systems $\mathbb N, \mathbb Z, \mathbb Q, \mathbb R, \mathbb C$ all have zero, but when zero is deleted from any of these sets the correct symbol for the result is $\mathbb N^*, \mathbb Z^*, \mathbb Q^*, \mathbb R^*, \mathbb C^*$. (This is superscript asterisk, not superscript times.) | |
| Oct 18, 2018 at 16:17 | comment | added | LSpice | A Google Books search mostly turns up the word "theorem" incidentally followed by the word "definition" (like "we'll prove the theorem. Definition 10.2 says …"), but here's an example from another source: (16.38) of Souriau - Structure of dynamical systems: A symplectic view of physics. | |
| Oct 18, 2018 at 16:12 | comment | added | LSpice | @EmanuelePaolini, it frequently occurs in Bourbaki. | |
| Oct 18, 2018 at 15:47 | answer | added | usul | timeline score: 2 | |
| Oct 18, 2018 at 11:07 | comment | added | Emanuele Paolini | @S.Carnahan (or anyone) can you point to some text where this label is used? | |
| Oct 17, 2018 at 15:54 | comment | added | LSpice | Although the rational-number example is clearly not the heart of your question, I'd like to agitate against $\mathbb Z^*$ for $\mathbb Z \setminus \{0\}$. In this context, it is clearly meant to be (identical to, or at least) reminiscent of the symbol $\times$, as in $\mathbb R^\times = \mathbb R \setminus \{0\}$; but $\times$ in this context should refer to the unit group, according to which $\mathbb Z^\times = \{\pm1\}$. The notation $\mathbb Z_{\ne0}$ is one, albeit ugly, alternative. | |
| Oct 17, 2018 at 13:06 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Oct 17, 2018 at 9:08 | comment | added | S. Carnahan♦ | These are often introduced with the label "Theorem-Definition" or "Lemma-Definition". | |
| Oct 17, 2018 at 7:11 | history | edited | Emanuele Paolini | CC BY-SA 4.0 |
added 24 characters in body
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| Oct 17, 2018 at 7:05 | history | asked | Emanuele Paolini | CC BY-SA 4.0 |