Re: MacOSX-TeX Digest, Vol 130, Issue 13

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Re: MacOSX-TeX Digest, Vol 130, Issue 13

Brian Coleman
Hi All,

\triangleq   works fine for me.

See attached example. 

Brian Coleman

On Tue, 21 Aug 2018 at 20:00, <[hidden email]> wrote:
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Today's Topics:

   1. Re: Latex symbol for "define equal" (Markus Klyver)
   2. Re: Latex symbol for "define equal" (Markus Klyver)
   3. Re: Latex symbol for "define equal" (juan tolosa)
   4. Re: Latex symbol for "define equal" (Josep Maria Font)
   5. Re: Latex symbol for "define equal" (Markus Klyver)
   6. Re: Latex symbol for "define equal" (Markus Klyver)
   7. Re: Latex symbol for "define equal" (Josep Maria Font)
   8. Re: Latex symbol for "define equal" (Ross Moore)
   9. Re: Latex symbol for "define equal" (Markus Klyver)
  10. Re: Latex symbol for "define equal" (Markus Klyver)
  11. Re: Latex symbol for "define equal" (Martin Berggren)
  12. Re: Latex symbol for "define equal" (N?stor E. Aguilera)
  13. Re: Latex symbol for "define equal" (N?stor E. Aguilera)
  14. Re: Latex symbol for "define equal" (Markus Klyver)
  15. Re: Latex symbol for "define equal" (Markus Klyver)
  16. Re: Latex symbol for "define equal" (Martin Berggren)


----------------------------------------------------------------------

Message: 1
Date: Mon, 20 Aug 2018 23:51:26 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="utf-8"

Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
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Message: 2
Date: Mon, 20 Aug 2018 23:56:02 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="utf-8"

Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
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Message: 3
Date: Mon, 20 Aug 2018 23:40:59 -0400
From: juan tolosa <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain; charset=utf-8

This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using ?if and only if? instead of plain ?if?, as in

 Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)

(Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)

One could simply agree that the ?if? in definitions is not the same as the ?if? in logical statements.
If one is really fastidious, one could put a statement at the beginning of the book that ?if? in definitions can be reworded as, say,
by ?(a_n) converges to p? we mean ? (etc)
Or simply not use ?if? at all in definitions.
What is even more annoying is that when the definition gets really involved, the ?if and only if? makes it even worse.
And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use ?if.?
Question is, why not do it from the very beginning?

Juan

> On Aug 20, 2018, at 7:56 PM, Markus Klyver <[hidden email]> wrote:
>
> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
> ----------- 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



------------------------------

Message: 4
Date: Tue, 21 Aug 2018 10:15:24 +0000
From: Josep Maria Font <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].


JMaF


> El 21 /08/18, a les 5:40, juan tolosa <[hidden email]> va escriure:
>
> This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using ?if and only if? instead of plain ?if?, as in
>
> Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)
>
> (Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)
>
> One could simply agree that the ?if? in definitions is not the same as the ?if? in logical statements.
> If one is really fastidious, one could put a statement at the beginning of the book that ?if? in definitions can be reworded as, say,
> by ?(a_n) converges to p? we mean ? (etc)
> Or simply not use ?if? at all in definitions.
> What is even more annoying is that when the definition gets really involved, the ?if and only if? makes it even worse.
> And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use ?if.?
> Question is, why not do it from the very beginning?
>
> Juan
>
>> On Aug 20, 2018, at 7:56 PM, Markus Klyver <[hidden email]> wrote:
>>
>> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
>> ----------- 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
>
> ----------- 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



Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informaci? confidencial o protegida legalment i s?adre?a exclusivament a la persona o entitat destinat?ria. Si no consteu com a destinatari final o no teniu l?enc?rrec de rebre?l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l?heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener informaci?n confidencial o legalmente protegida y est? exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no est? autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.

This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.

------------------------------

Message: 5
Date: Tue, 21 Aug 2018 10:40:21 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="windows-1252"

This will be a little rant, but I completely disagree with you. It annoys me when authors *don't* use "iff" in definitions, and here's why:


P if Q means that Q implies P. But in the case of definitions, it's a fact of an equivalence. We mean P <---> Q, which also is the meaning of "iff". Using only "if" in definitions causes confusion. Consider the following example: x=0 if f(x)=0. Do we mean this as something we derived, that x=0 implies f(x)=0? Or do we mean it as a definition of the function f, that f is defined to have only one root x=0?  Since definitions are implications both ways, one should use "iff" and not "if".


It all has to do with the fact that natural language is really bad to state mathematical facts in; and non-mathematicians (like engineers) totally fail to see this point because they are not trained in logic or how a logical statement looks like.


________________________________
Fr?n: MacOSX-TeX <[hidden email]> f?r juan tolosa <[hidden email]>
Skickat: den 21 augusti 2018 05:40
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using ?if and only if? instead of plain ?if?, as in

 Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)

(Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)

One could simply agree that the ?if? in definitions is not the same as the ?if? in logical statements.
If one is really fastidious, one could put a statement at the beginning of the book that ?if? in definitions can be reworded as, say,
by ?(a_n) converges to p? we mean ? (etc)
Or simply not use ?if? at all in definitions.
What is even more annoying is that when the definition gets really involved, the ?if and only if? makes it even worse.
And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use ?if.?
Question is, why not do it from the very beginning?

Juan

> On Aug 20, 2018, at 7:56 PM, Markus Klyver <[hidden email]> wrote:
>
> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
> ----------- 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

----------- 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/
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Message: 6
Date: Tue, 21 Aug 2018 11:02:03 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="windows-1252"

But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?


________________________________
Fr?n: MacOSX-TeX <[hidden email]> f?r Josep Maria Font <[hidden email]>
Skickat: den 21 augusti 2018 12:15
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].


JMaF


> El 21 /08/18, a les 5:40, juan tolosa <[hidden email]> va escriure:
>
> This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using ?if and only if? instead of plain ?if?, as in
>
> Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)
>
> (Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)
>
> One could simply agree that the ?if? in definitions is not the same as the ?if? in logical statements.
> If one is really fastidious, one could put a statement at the beginning of the book that ?if? in definitions can be reworded as, say,
> by ?(a_n) converges to p? we mean ? (etc)
> Or simply not use ?if? at all in definitions.
> What is even more annoying is that when the definition gets really involved, the ?if and only if? makes it even worse.
> And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use ?if.?
> Question is, why not do it from the very beginning?
>
> Juan
>
>> On Aug 20, 2018, at 7:56 PM, Markus Klyver <[hidden email]> wrote:
>>
>> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
>> ----------- 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
>
> ----------- 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



Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informaci? confidencial o protegida legalment i s?adre?a exclusivament a la persona o entitat destinat?ria. Si no consteu com a destinatari final o no teniu l?enc?rrec de rebre?l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l?heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener informaci?n confidencial o legalmente protegida y est? exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no est? autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.

This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.
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Message: 7
Date: Tue, 21 Aug 2018 11:12:27 +0000
From: Josep Maria Font <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

If the context does not make it clear whether you are reading a theorem or a definition, something is wrong with this book !

Normally the reader is reading a statement marked as "Definition", or one marked as "Theorem" (Lemma, Proposition, etc.). And in the Preliminaries you can explain your usage of "when" in definitions as meaning "if and only if".

In this way you keep the "if" family, including "if and only if", for real mathematical statements, that is, statements which you can (in theory) check whether they are true or false; notice that one of the main differences between a definition and a theorem is that it does not make sense to say that a definition is true or false!


JMaF


El 21 /08/18, a les 13:02, Markus Klyver <[hidden email]<mailto:[hidden email]>> va escriure:

But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?


________________________________
Fr?n: MacOSX-TeX <[hidden email]<mailto:[hidden email]>> f?r Josep Maria Font <[hidden email]<mailto:[hidden email]>>
Skickat: den 21 augusti 2018 12:15
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].


JMaF


> El 21 /08/18, a les 5:40, juan tolosa <[hidden email]<mailto:[hidden email]>> va escriure:
>
> This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using ?if and only if? instead of plain ?if?, as in
>
> Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)
>
> (Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)
>
> One could simply agree that the ?if? in definitions is not the same as the ?if? in logical statements.
> If one is really fastidious, one could put a statement at the beginning of the book that ?if? in definitions can be reworded as, say,
> by ?(a_n) converges to p? we mean ? (etc)
> Or simply not use ?if? at all in definitions.
> What is even more annoying is that when the definition gets really involved, the ?if and only if? makes it even worse.
> And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use ?if.?
> Question is, why not do it from the very beginning?
>
> Juan
>
>> On Aug 20, 2018, at 7:56 PM, Markus Klyver <[hidden email]<mailto:[hidden email]>> wrote:
>>
>> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
>> ----------- 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
>
> ----------- 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



Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informaci? confidencial o protegida legalment i s?adre?a exclusivament a la persona o entitat destinat?ria. Si no consteu com a destinatari final o no teniu l?enc?rrec de rebre?l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l?heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener informaci?n confidencial o legalmente protegida y est? exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no est? autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.

This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.
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Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informaci? confidencial o protegida legalment i s?adre?a exclusivament a la persona o entitat destinat?ria. Si no consteu com a destinatari final o no teniu l?enc?rrec de rebre?l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l?heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

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Message: 8
Date: Tue, 21 Aug 2018 11:21:34 +0000
From: Ross Moore <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Cc: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

Hi all.

I agree with using "when", or better "precisely when", in definitions.
Do not use these words in theorems. There are many alternative ways to express what you want.

But didn't this thread start out asking for a symbolic notation?
In that context, equivalence is *not* the word you want for a definition, as equivalence depends on a particular relation, so is weaker than a definition.

There are nuances in mathematical concepts and notations that are not always correctly appreciated by those who work primarily in other (mostly applied) fields.


On 21/08/2018, at 13:03, "Markus Klyver" <[hidden email]<mailto:[hidden email]>> wrote:


But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?


________________________________
Fr?n: MacOSX-TeX <[hidden email]<mailto:[hidden email]>> f?r Josep Maria Font <[hidden email]<mailto:[hidden email]>>
Skickat: den 21 augusti 2018 12:15
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].


JMaF


Cheers,

   Ross
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Message: 9
Date: Tue, 21 Aug 2018 11:47:26 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="windows-1252"

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 linear independent eigenvectors, Ax=0 only having the trivial solution, Ax=b having a solution (which is unique) for every right-hand-side b, etc.


In these cases it doesn't make much sense to use "if" and lose the importance that all these other statements, which could be taken as definitions. are equivalent. An other example: consider what it means for a complex to be holomorphic. It turns out that holomorphic and analytical is the same for complex functions, but it's not the same on R. You can have a real smooth non-analytical function, so clearly one should be careful to treat those concepts as the same. Which is why you keep "iff" in the definition of holomorphicy, not fooling students that entire and analytical functions are the same.


________________________________
Fr?n: MacOSX-TeX <[hidden email]> f?r Josep Maria Font <[hidden email]>
Skickat: den 21 augusti 2018 13:12
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

If the context does not make it clear whether you are reading a theorem or a definition, something is wrong with this book !

Normally the reader is reading a statement marked as "Definition", or one marked as "Theorem" (Lemma, Proposition, etc.). And in the Preliminaries you can explain your usage of "when" in definitions as meaning "if and only if".

In this way you keep the "if" family, including "if and only if", for real mathematical statements, that is, statements which you can (in theory) check whether they are true or false; notice that one of the main differences between a definition and a theorem is that it does not make sense to say that a definition is true or false!


JMaF


El 21 /08/18, a les 13:02, Markus Klyver <[hidden email]<mailto:[hidden email]>> va escriure:

But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?


________________________________
Fr?n: MacOSX-TeX <[hidden email]<mailto:[hidden email]>> f?r Josep Maria Font <[hidden email]<mailto:[hidden email]>>
Skickat: den 21 augusti 2018 12:15
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].


JMaF


> El 21 /08/18, a les 5:40, juan tolosa <[hidden email]<mailto:[hidden email]>> va escriure:
>
> This is tangential but, since we are at it, what really, really annoys me, is the tendency in some books to define concepts using ?if and only if? instead of plain ?if?, as in
>
> Definition. A sequence (a_n) converges to a real number p if and only if for every epsilon > 0 there is an N such that (etc.)
>
> (Is it my impression, or there is a growing number of such texts? And when did this nonsense begin?)
>
> One could simply agree that the ?if? in definitions is not the same as the ?if? in logical statements.
> If one is really fastidious, one could put a statement at the beginning of the book that ?if? in definitions can be reworded as, say,
> by ?(a_n) converges to p? we mean ? (etc)
> Or simply not use ?if? at all in definitions.
> What is even more annoying is that when the definition gets really involved, the ?if and only if? makes it even worse.
> And, invariably, in a really involved definition you will find that the author(s) abandon their own fastidiousness and just use ?if.?
> Question is, why not do it from the very beginning?
>
> Juan
>
>> On Aug 20, 2018, at 7:56 PM, Markus Klyver <[hidden email]<mailto:[hidden email]>> wrote:
>>
>> Really, there's no standardized notation for it. Just be consistent and use the most aesthetically pleasing and practical notation on your context. Maybe := looks ugly will your fonts. Use an other notation instead.
>> ----------- Please Consult the Following Before Posting -----------
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Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informaci? confidencial o protegida legalment i s?adre?a exclusivament a la persona o entitat destinat?ria. Si no consteu com a destinatari final o no teniu l?enc?rrec de rebre?l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l?heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener informaci?n confidencial o legalmente protegida y est? exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no est? autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.

This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.
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Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informaci? confidencial o protegida legalment i s?adre?a exclusivament a la persona o entitat destinat?ria. Si no consteu com a destinatari final o no teniu l?enc?rrec de rebre?l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l?heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener informaci?n confidencial o legalmente protegida y est? exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no est? autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.

This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.
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Message: 10
Date: Tue, 21 Aug 2018 11:49:09 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="iso-8859-1"

Definitions *are* equivalences.


________________________________
Fr?n: MacOSX-TeX <[hidden email]> f?r Ross Moore <[hidden email]>
Skickat: den 21 augusti 2018 13:21
Till: TeX on Mac OS X Mailing List
Kopia: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

Hi all.

I agree with using "when", or better "precisely when", in definitions.
Do not use these words in theorems. There are many alternative ways to express what you want.

But didn't this thread start out asking for a symbolic notation?
In that context, equivalence is *not* the word you want for a definition, as equivalence depends on a particular relation, so is weaker than a definition.

There are nuances in mathematical concepts and notations that are not always correctly appreciated by those who work primarily in other (mostly applied) fields.


On 21/08/2018, at 13:03, "Markus Klyver" <[hidden email]<mailto:[hidden email]>> wrote:


But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?


________________________________
Fr?n: MacOSX-TeX <[hidden email]<mailto:[hidden email]>> f?r Josep Maria Font <[hidden email]<mailto:[hidden email]>>
Skickat: den 21 augusti 2018 12:15
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].


JMaF


Cheers,

   Ross
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Message: 11
Date: Tue, 21 Aug 2018 13:59:18 +0200
From: Martin Berggren <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"


> On 21 Aug 2018, at 13:47, Markus Klyver <[hidden email]> 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.

Sincerely,


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


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Message: 12
Date: Tue, 21 Aug 2018 09:10:57 -0300
From: "N?stor E. Aguilera" <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain;       charset=utf-8

Hi everyone:

It seems to me that when we use "=" or another symbol in a "definition" we are actually stablishin a "notation". When we say "A is invertible if/iff/when..." this looks more like a definition, but it is actually a naming convention (right?), that is, a variant of notation, where we use a name to describe a perhaps complex situation.

Knuth "defines" (as stated in Appendix B) the "bracket notation" (ACP, Vol 1, ?1.2.3, equation (16)) using "=" and "if".

Perhaps somebody can explain what are the differences, if any, between "definition" and "notation".

Best,

Nestor

===============================================

> On 21 Aug 2018, at 08:49, Markus Klyver <[hidden email]> wrote:
>
> Definitions *are* equivalences.
>
>
> Fr?n: MacOSX-TeX <[hidden email]> f?r Ross Moore <[hidden email]>
> Skickat: den 21 augusti 2018 13:21
> Till: TeX on Mac OS X Mailing List
> Kopia: TeX on Mac OS X Mailing List
> ?mne: Re: [OS X TeX] Latex symbol for "define equal"

> Hi all.
>
> I agree with using "when", or better "precisely when", in definitions.
> Do not use these words in theorems. There are many alternative ways to express what you want.
>
> But didn't this thread start out asking for a symbolic notation?
> In that context, equivalence is *not* the word you want for a definition, as equivalence depends on a particular relation, so is weaker than a definition.
>
> There are nuances in mathematical concepts and notations that are not always correctly appreciated by those who work primarily in other (mostly applied) fields.
>
>
> On 21/08/2018, at 13:03, "Markus Klyver" <[hidden email]> wrote:
>
>> But how would the reader know if it's a theorem or a definition? Consider the statement "f(x)=1 when x=2". Do we mean f(x)=1 <---> x=2 or just f(x)=1 <--- x=2?
>>
>>
>> Fr?n: MacOSX-TeX <[hidden email]> f?r Josep Maria Font <[hidden email]>
>> Skickat: den 21 augusti 2018 12:15
>> Till: TeX on Mac OS X Mailing List
>> ?mne: Re: [OS X TeX] Latex symbol for "define equal"
>> 
>> That's why I prefer to use "when" for definitions: [...this NEW thing happens...] WHEN [...such-and-such known, understandable condition holds...].
>>
>>
>> JMaF
>
>
> Cheers,
>
>    Ross
> ----------- 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/
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> List Info: https://email.esm.psu.edu/mailman/listinfo/macosx-tex



------------------------------

Message: 13
Date: Tue, 21 Aug 2018 09:43:39 -0300
From: "N?stor E. Aguilera" <[hidden email]>
To: Ralph Martin <[hidden email]>
Cc: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain;       charset=utf-8

Hi Ralph:

> On 21 Aug 2018, at 09:30, Ralph Martin <[hidden email]> wrote:
>
>> [...]
>
> Definitions give *names* for concepts:
> - a "matrix" is a two-dimensional table ...
> - an "invertible matrix" is a matrix which ...
>
> Notation gives *symbols* for concepts (or quantities):
> - ? is used to denote the ratio of the circumference of any circle to its diameter
> - t is used to denote time
> - boldface letters are used to denote vectors
>
> I always have trouble getting computer science students not to use multi-letter variable *names* in maths, when they should be using *symbols* for variables.

So, would you say that the equality sign (or some replacement of it) in a "definition" is actually describing a "notation"?

Nestor

------------------------------

Message: 14
Date: Tue, 21 Aug 2018 12:48:48 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="windows-1252"

Depends, literature tends to use the definitions interchangeably depending on what aspect is important to subject.


________________________________
Fr?n: MacOSX-TeX <[hidden email]> f?r Martin Berggren <[hidden email]>
Skickat: den 21 augusti 2018 13:59
Till: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"


On 21 Aug 2018, at 13:47, Markus Klyver <[hidden email]<mailto:[hidden email]>> 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.

Sincerely,


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


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Message: 15
Date: Tue, 21 Aug 2018 12:51:48 +0000
From: Markus Klyver <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID:
        <[hidden email]>

Content-Type: text/plain; charset="utf-8"

Yes, the sign = usually denotes an equivalence relation between two sets of interest. So the equality sign is a matter of notation, denoting "equality" (in the sense of an equivalence relation).


________________________________
Fr?n: MacOSX-TeX <[hidden email]> f?r "N?stor E. Aguilera" <[hidden email]>
Skickat: den 21 augusti 2018 14:43
Till: Ralph Martin
Kopia: TeX on Mac OS X Mailing List
?mne: Re: [OS X TeX] Latex symbol for "define equal"

Hi Ralph:

> On 21 Aug 2018, at 09:30, Ralph Martin <[hidden email]> wrote:
>
>> [...]
>
> Definitions give *names* for concepts:
> - a "matrix" is a two-dimensional table ...
> - an "invertible matrix" is a matrix which ...
>
> Notation gives *symbols* for concepts (or quantities):
> - ? is used to denote the ratio of the circumference of any circle to its diameter
> - t is used to denote time
> - boldface letters are used to denote vectors
>
> I always have trouble getting computer science students not to use multi-letter variable *names* in maths, when they should be using *symbols* for variables.

So, would you say that the equality sign (or some replacement of it) in a "definition" is actually describing a "notation"?

Nestor
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Message: 16
Date: Tue, 21 Aug 2018 14:58:46 +0200
From: Martin Berggren <[hidden email]>
To: TeX on Mac OS X Mailing List <[hidden email]>
Subject: Re: [OS X TeX] Latex symbol for "define equal"
Message-ID: <[hidden email]>
Content-Type: text/plain; charset="utf-8"

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 <[hidden email]> wrote:
>
> Depends, literature tends to use the definitions interchangeably depending on what aspect is important to subject.
>
>
> Fr?n: MacOSX-TeX <[hidden email] <mailto:[hidden email]>> f?r Martin Berggren <[hidden email] <mailto:[hidden email]>>
> Skickat: den 21 augusti 2018 13:59
> Till: TeX on Mac OS X Mailing List
> ?mne: Re: [OS X TeX] Latex symbol for "define equal"

>
>> On 21 Aug 2018, at 13:47, Markus Klyver <[hidden email] <mailto:[hidden email]>> 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
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Re: MacOSX-TeX Digest, Vol 130, Issue 13

Martin Wilhelm Leidig-2
> Today's Topics:

>
>    1. Re: Latex symbol for "define equal" (Markus Klyver)
>    2. Re: Latex symbol for "define equal" (Markus Klyver)
>    3. Re: Latex symbol for "define equal" (juan tolosa)
>    4. Re: Latex symbol for "define equal" (Josep Maria Font)
>    5. Re: Latex symbol for "define equal" (Markus Klyver)
>    6. Re: Latex symbol for "define equal" (Markus Klyver)
>    7. Re: Latex symbol for "define equal" (Josep Maria Font)
>    8. Re: Latex symbol for "define equal" (Ross Moore)
>    9. Re: Latex symbol for "define equal" (Markus Klyver)
>   10. Re: Latex symbol for "define equal" (Markus Klyver)
>   11. Re: Latex symbol for "define equal" (Martin Berggren)
>   12. Re: Latex symbol for "define equal" (N?stor E. Aguilera)
>   13. Re: Latex symbol for "define equal" (N?stor E. Aguilera)
>   14. Re: Latex symbol for "define equal" (Markus Klyver)
>   15. Re: Latex symbol for "define equal" (Markus Klyver)
>   16. Re: Latex symbol for "define equal" (Martin Berggren)
[full text of 16 list mails snipped]

Really, man!?  m(


Regards,

-Moss-
--
Martin Wilhelm Leidig


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