[OS X TeX] Latex symbol for "define equal"

[Martin Berggren]

Regarding the difference between a theorem and a definition: In the words of my thesis advisor: You cannot argue with a definition. (It should be said with a french accent!) A definition can be nice, practical, useful, or impractical, unnecessary, confusing, and so on, but it cannot be true or false. A theorem, however, is true.

Cheers,

> On 21 Aug 2018, at 14:48, Markus Klyver <markusklyver at hotmail.com> wrote:
> 
> Depends, literature tends to use the definitions interchangeably depending on what aspect is important to subject.
> 
> 
> Från: MacOSX-TeX <macosx-tex-bounces at email.esm.psu.edu <mailto:macosx-tex-bounces at email.esm.psu.edu>> för Martin Berggren <martin.berggren at cs.umu.se <mailto:martin.berggren at cs.umu.se>>
> Skickat: den 21 augusti 2018 13:59
> Till: TeX on Mac OS X Mailing List
> Ämne: Re: [OS X TeX] Latex symbol for "define equal"
>  
> 
>> On 21 Aug 2018, at 13:47, Markus Klyver <markusklyver at hotmail.com <mailto:markusklyver at hotmail.com>> wrote:
>> 
>> The thing is that you can have several different definitions, all equivalent.  Consider the definition "a matrix A \in \mathbb R^{n \times n} is invertiable iff A have a multiplicative inverse". It turns out that this is equivalent to a lot of things, among det(A) !=0, A having full rang, A having n linearindependent eigenvectors, Ax=0 only having the trivial solution, Ax=b having a solution (which is unique) for every right-hand-side b, etc.
> 
> I would save that this is a theorem, not a definition. I think of a definition as a “macro”; that is,  giving a short name to a mathematical property. Example: a matrix A is called positive semidefinite when x^T Ax \geq 0 for all vectors x. The point is that you in each instances when the name is used, it can be replaced by its definition. 
> 

Martin Berggren
-------------------------------------------------------------------
Department of Computing Science, 
UMIT Research Lab
Umeå Universitet
Campustorget 5, S-901 87 Umeå, Sweden. Ph: +46-70-732 8111
http://www.cs.umu.se/~martinb <http://www.cs.umu.se/~martinb>, Martin.Berggren at cs.umu.se <mailto:Martin.Berggren at cs.umu.se>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://tug.org/pipermail/macostex-archives/attachments/20180821/d1b74865/attachment.html>
-------------- next part --------------
----------- Please Consult the Following Before Posting -----------
TeX FAQ: http://www.tex.ac.uk/faq
List Reminders and Etiquette: https://sites.esm.psu.edu/~gray/tex/
List Archives: http://dir.gmane.org/gmane.comp.tex.macosx
                https://email.esm.psu.edu/pipermail/macosx-tex/
TeX on Mac OS X Website: http://mactex-wiki.tug.org/
List Info: https://email.esm.psu.edu/mailman/listinfo/macosx-tex