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

Martin Berggren martin.berggren at cs.umu.se
Tue Aug 21 14:58:46 CEST 2018

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.


> 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>

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