Latex symbol for "define equal"

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Latex symbol for "define equal"

Themis Matsoukas-6
What is the accepted symbol in math for “equal by definition” and how to get in latex? I have been using \equiv but I have seen “:=“, equal sign with a triangle on top, or “def” on top of =.

Themis



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Re: Latex symbol for "define equal"

Gray, Gary L
> On Aug 18, 2018, at 7:21 AM, Themis Matsoukas <[hidden email]> wrote:
>
> What is the accepted symbol in math for “equal by definition” and how to get in latex? I have been using \equiv but I have seen “:=“, equal sign with a triangle on top, or “def” on top of =.

I have seen it done in many ways, but I have always used \equiv. I would simply state that when that symbol is used, it means “equal to by definition”.

Gary
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Re: Latex symbol for "define equal"

Themis Matsoukas-6
> On Aug 18, 2018, at 9:46 AM, Gary L. Gray <[hidden email]> wrote:
>
>> On Aug 18, 2018, at 7:21 AM, Themis Matsoukas <[hidden email]> wrote:
>>
>> What is the accepted symbol in math for “equal by definition” and how to get in latex? I have been using \equiv but I have seen “:=“, equal sign with a triangle on top, or “def” on top of =.
>
> I have seen it done in many ways, but I have always used \equiv. I would simply state that when that symbol is used, it means “equal to by definition”.
>
> Gary

Its good to know that \equiv is acceptable.

Thanks

Themis

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Re: Latex symbol for "define equal"

Art Werschulz
In reply to this post by Themis Matsoukas-6
Hi.

> On Aug 18, 2018, at 7:21 AM, Themis Matsoukas <[hidden email]> wrote:
>
> What is the accepted symbol in math for “equal by definition” and how to get in latex? I have been using \equiv but I have seen “:=“, equal sign with a triangle on top, or “def” on top of =.

I'm used to seeing := as the notation for "is defined to be".  You sometimes find =: for "defines", when it's more natural to have the thing being defined at the end, rather than at the beginning, of a math passage.

The centercolon and mathtools LaTeX packages are used to fix symmetry issues with := .

BTW, the last time I used \equiv for defining something (something like $E_{d,\gamma}f\equiv f$, a referee swatted it down.  :=)

Art Werschulz
[hidden email]



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Re: Latex symbol for "define equal"

Enrico Franconi-3
In our community, definitions are introduced with \doteq 
--e.

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Re: Latex symbol for "define equal"

Themis Matsoukas-6
In reply to this post by Art Werschulz

> BTW, the last time I used \equiv for defining something (something like $E_{d,\gamma}f\equiv f$, a referee swatted it down.  :=)
>

…and good to know that \equiv is unacceptable :)

I suppose there is an orthodoxy with its high priesthood etc. in every human institution. I’m not trying to be orthodox on this, just not too radical.

Themis

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Re: Latex symbol for "define equal"

Vic Norton
In reply to this post by Art Werschulz

> On Aug 18, 2018, at 10:01 PM, Art Werschulz <[hidden email]> wrote:
>
> The centercolon and mathtools LaTeX packages are used to fix symmetry issues with := .

In Pascal and Algol := is the assignment operator. The phrase x := 2 means “set x equal to 2". I personally would avoid using := for any other purpose in LaTeX.

Vic
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Re: Latex symbol for "define equal"

Ettore Aldrovandi
In reply to this post by Themis Matsoukas-6

On Aug 19, 2018, at 05:53, Themis Matsoukas <[hidden email]> wrote:


BTW, the last time I used \equiv for defining something (something like $E_{d,\gamma}f\equiv f$, a referee swatted it down.  :=)


…and good to know that \equiv is unacceptable :)

I tend to not use \equiv, but rather favor := (or even = with ‘def’ on top) for an “equal by definition,” where in effect the term on the left is introduced for the first time. The \equiv lends itself better to express an identity between two terms. In other words, and extending a bit, \equiv expresses the idea of a “canonical isomorphism,” and therefore \cong (or some such) just is an isomorphism.

My two math cents.

—Ettore

Ettore Aldrovandi
Department of Mathematics, Florida State University
1017 Academic Way                *   http://www.math.fsu.edu/~ealdrov
Tallahassee, FL 32306-4510, USA * * aldrovandi at math dot fsu dot edu


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Re: Latex symbol for "define equal"

Martin Bergren
= with def on top can be accomplished with

\newcommand{\defn}{\stackrel{\textrm{\scriptsize def}}{=}}

Or, if you don’t like the extra space that the presence of the text yields you can do

\newcommand{\defn}{\stackrel{\textrm{\clap{\scriptsize def}}}{=}}


Usage: 

These defines a to be b: $a\defn b$,  $a\defnn b$.


Cheers,

Martin Berggren
-------------------------------------------------------------------
Department of Computing Science, Umeå Universitet
Campustorget 5, S-901 87 Umeå, Sweden. Ph: +46-70-732 8111
http://www.cs.umu.se/~martinb[hidden email]


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Re: Latex symbol for "define equal"

R Martinez
In reply to this post by Vic Norton
I believe that Don Knuth favors using the plain equals sign = for everything including definitions. I read it somewhere but can’t recall the source. One bit of evidence is that in his book “Concrete Mathematics” the floor and ceiling functions are defined using the equals sign (1989 edition, page. 67).

Raul Martinez

> On Aug 19, 2018, at 3:28 AM, Vic Norton <[hidden email]> wrote:
>
>
>> On Aug 18, 2018, at 10:01 PM, Art Werschulz <[hidden email]> wrote:
>>
>> The centercolon and mathtools LaTeX packages are used to fix symmetry issues with := .
>
> In Pascal and Algol := is the assignment operator. The phrase x := 2 means “set x equal to 2". I personally would avoid using := for any other purpose in LaTeX.
> —
> Vic
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Re: Latex symbol for "define equal"

Josep Maria Font-2
In logic and universal algebra, and in general in disciplines where the equals sign = can be not just a symbol but a mathematical object by itself, some people (including me :-) find it useful to have a special equals symbol which means "equal by definition". I have been using := , and for this the "mathtools" package offers a fine solution, the macro \coloneqq, which places the : symmetrically wrt the axis of the = symbol (something you do not obtain by just writing := !).

And I find this usage somehow comparable to the "assignment" usage of programming languages; only that here we are "assigning a meaning" to a previously void symbol or complex of symbols.


JMaF



> El 19 /08/18, a les 23:50, R Martinez <[hidden email]> va escriure:
>
> I believe that Don Knuth favors using the plain equals sign = for everything including definitions. I read it somewhere but can’t recall the source. One bit of evidence is that in his book “Concrete Mathematics” the floor and ceiling functions are defined using the equals sign (1989 edition, page. 67).
>
> Raul Martinez
>
>> On Aug 19, 2018, at 3:28 AM, Vic Norton <[hidden email]> wrote:
>>
>>
>>> On Aug 18, 2018, at 10:01 PM, Art Werschulz <[hidden email]> wrote:
>>>
>>> The centercolon and mathtools LaTeX packages are used to fix symmetry issues with := .
>>
>> In Pascal and Algol := is the assignment operator. The phrase x := 2 means “set x equal to 2". I personally would avoid using := for any other purpose in LaTeX.
>> —
>> Vic
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>
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Re: Latex symbol for "define equal"

David Derbes
I and several colleagues just finished editing a 1200 page manuscript, LaTeX’d lectures of the great Sidney Coleman on quantum field theory. One of the colleagues was the well-known physicist author David Griffiths, who earned his doctorate under Coleman. He championed \equiv for “defined as”, and I think that is pretty standard in physics. It appears perhaps two dozen times in the Coleman lectures.

I’m an old Pascal programmer (there are probably not that many young Pascal programmers :-) ) and while I love :=, I don’t see it catching on as “defined as”, notwithstanding the impeccable logic of JMaF. I have never seen it used that way in physics (but that doesn’t mean it hasn’t been).

David Derbes
U of Chicago Lab Schools


On Aug 19, 2018, at 17:05, Josep Maria Font <[hidden email]> wrote:

> In logic and universal algebra, and in general in disciplines where the equals sign = can be not just a symbol but a mathematical object by itself, some people (including me :-) find it useful to have a special equals symbol which means "equal by definition". I have been using := , and for this the "mathtools" package offers a fine solution, the macro \coloneqq, which places the : symmetrically wrt the axis of the = symbol (something you do not obtain by just writing := !).
>
> And I find this usage somehow comparable to the "assignment" usage of programming languages; only that here we are "assigning a meaning" to a previously void symbol or complex of symbols.
>
>
> JMaF
>
>
>
>> El 19 /08/18, a les 23:50, R Martinez <[hidden email]> va escriure:
>>
>> I believe that Don Knuth favors using the plain equals sign = for everything including definitions. I read it somewhere but can’t recall the source. One bit of evidence is that in his book “Concrete Mathematics” the floor and ceiling functions are defined using the equals sign (1989 edition, page. 67).
>>
>> Raul Martinez
>>
>>> On Aug 19, 2018, at 3:28 AM, Vic Norton <[hidden email]> wrote:
>>>
>>>
>>>> On Aug 18, 2018, at 10:01 PM, Art Werschulz <[hidden email]> wrote:
>>>>
>>>> The centercolon and mathtools LaTeX packages are used to fix symmetry issues with := .
>>>
>>> In Pascal and Algol := is the assignment operator. The phrase x := 2 means “set x equal to 2". I personally would avoid using := for any other purpose in LaTeX.
>>> —
>>> Vic
>>> ----------- Please Consult the Following Before Posting -----------
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>>
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>
>
>
> Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final o no teniu l’encàrrec 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 información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no está 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.
>
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Re: Latex symbol for "define equal"

Herbert Schulz
> On Aug 19, 2018, at 5:43 PM, David Derbes <[hidden email]> wrote:
>
> I and several colleagues just finished editing a 1200 page manuscript, LaTeX’d lectures of the great Sidney Coleman on quantum field theory. One of the colleagues was the well-known physicist author David Griffiths, who earned his doctorate under Coleman. He championed \equiv for “defined as”, and I think that is pretty standard in physics. It appears perhaps two dozen times in the Coleman lectures.
>
> I’m an old Pascal programmer (there are probably not that many young Pascal programmers :-) ) and while I love :=, I don’t see it catching on as “defined as”, notwithstanding the impeccable logic of JMaF. I have never seen it used that way in physics (but that doesn’t mean it hasn’t been).
>
> David Derbes
> U of Chicago Lab Schools

Howdy,

I've always assumed Pascal's use of := rather than = as ``assigned to'' is because

x = x + 1

used to increment a memory location assigned the name x makes no sense as a mathematical equation but

x := x + 1

makes sense.

Good Luck,

Herb Schulz
(herbs at wideopenwest dot com)

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Re: Latex symbol for "define equal"

Art Werschulz
Hi.

> On Aug 19, 2018, at 6:52 PM, Herbert Schulz <[hidden email]> wrote:
>
> I've always assumed Pascal's use of := rather than = as ``assigned to'' is because
>
> x = x + 1
>
> used to increment a memory location assigned the name x makes no sense as a mathematical equation but
>
> x := x + 1
>
> makes sense.

The := was used for the assignment operator in Algol; you can see it in the Algol 58 Report.  (Algol was the second programming language I learned, Fortran being the first.)

As I understand it, the reason C used = rather than := for assignment was that assignment statements were more common than comparing for equality, so the more easily-typed operator was used for the more common operation.

Art Werschulz
[hidden email]



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Re: Latex symbol for "define equal"

Markus Klyver
In reply to this post by Themis Matsoukas-6
In mathematics, we often use := to denote equality by definition.

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Re: Latex symbol for "define equal"

Peter Teeson
Ken Iverson's APL programming language uses the leftwards arrow glyph for assign; e.g. A ← 3 5⍴ 1 2 3 or A←”I am a string” etc.
Unicode U+2190 UTF-8 E2 86 90    FWIW

> On Aug 20, 2018, at 8:11 AM, Markus Klyver <[hidden email]> wrote:
>
> In mathematics, we often use := to denote equality by definition.
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Re: Latex symbol for "define equal"

Markus Klyver
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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Re: Latex symbol for "define equal"

Markus Klyver
In reply to this post by Peter Teeson
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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Re: Latex symbol for "define equal"

juan tolosa
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.
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Re: Latex symbol for "define equal"

Josep Maria Font-2
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
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>>               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
>
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