Notation for “such that” on a set-builder notation












0












$begingroup$


This may be a really simple question to answer, but I need to know, with references to prove my affirmation, that the actual notation for "such that" on a set builder notation is the colon or vertical line, but not the oblique line. Can anybody help me with some reference for this notation?
Thank you very very much.






elementary-set-theory reference-request notation







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    You want references for that? Set builder notation is $textbf{notation}$: i.e., if you want to use a different symbol, go for it.
    $endgroup$
    – Don Thousand
    Dec 14 '18 at 3:42






  • 2




    $begingroup$
    There are many cases where people use nonstandard notation. As long as it is established before hand that the people are using the same notation it is okay. Rather then "actual notation" it might be better to say "standard notation" or "most commonly used notation"
    $endgroup$
    – Q the Platypus
    Dec 14 '18 at 3:44










  • $begingroup$
    Thank you for your comments. I was serching for references that establishes the vertical line or colon as standard notation, and that gives some reason for not using "/" instead of the other ones. This notation is going to be use on a very elementary material for school students.
    $endgroup$
    – Irene
    Dec 14 '18 at 11:47






  • 1




    $begingroup$
    You could make up reasons why $/$ is a bad choice, but you could just as well make up such reasons for $:$ and $|$. The real reason is just that it's the notation that everyone else uses. In any case, it seems rather bizarre that you need a reference to "prove" this, especially if this is just for students.
    $endgroup$
    – Eric Wofsey
    Dec 15 '18 at 22:14










  • $begingroup$
    It never occurred to me that the ":" in the weirdly-named "set-builder" notation was the mathematical notation for "such that". I suppose, then, that "{" is the notation for "the set of all", but what does "}" stand for?
    $endgroup$
    – bof
    Dec 15 '18 at 23:56
















0












$begingroup$


This may be a really simple question to answer, but I need to know, with references to prove my affirmation, that the actual notation for "such that" on a set builder notation is the colon or vertical line, but not the oblique line. Can anybody help me with some reference for this notation?
Thank you very very much.






elementary-set-theory reference-request notation







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    You want references for that? Set builder notation is $textbf{notation}$: i.e., if you want to use a different symbol, go for it.
    $endgroup$
    – Don Thousand
    Dec 14 '18 at 3:42






  • 2




    $begingroup$
    There are many cases where people use nonstandard notation. As long as it is established before hand that the people are using the same notation it is okay. Rather then "actual notation" it might be better to say "standard notation" or "most commonly used notation"
    $endgroup$
    – Q the Platypus
    Dec 14 '18 at 3:44










  • $begingroup$
    Thank you for your comments. I was serching for references that establishes the vertical line or colon as standard notation, and that gives some reason for not using "/" instead of the other ones. This notation is going to be use on a very elementary material for school students.
    $endgroup$
    – Irene
    Dec 14 '18 at 11:47






  • 1




    $begingroup$
    You could make up reasons why $/$ is a bad choice, but you could just as well make up such reasons for $:$ and $|$. The real reason is just that it's the notation that everyone else uses. In any case, it seems rather bizarre that you need a reference to "prove" this, especially if this is just for students.
    $endgroup$
    – Eric Wofsey
    Dec 15 '18 at 22:14










  • $begingroup$
    It never occurred to me that the ":" in the weirdly-named "set-builder" notation was the mathematical notation for "such that". I suppose, then, that "{" is the notation for "the set of all", but what does "}" stand for?
    $endgroup$
    – bof
    Dec 15 '18 at 23:56














0












0








0





$begingroup$


This may be a really simple question to answer, but I need to know, with references to prove my affirmation, that the actual notation for "such that" on a set builder notation is the colon or vertical line, but not the oblique line. Can anybody help me with some reference for this notation?
Thank you very very much.






elementary-set-theory reference-request notation







share|cite|improve this question











$endgroup$




This may be a really simple question to answer, but I need to know, with references to prove my affirmation, that the actual notation for "such that" on a set builder notation is the colon or vertical line, but not the oblique line. Can anybody help me with some reference for this notation?
Thank you very very much.






elementary-set-theory reference-request notation




elementary-set-theory reference-request notation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 14 '18 at 4:00









Andrés E. Caicedo

65.4k8158248




65.4k8158248










asked Dec 14 '18 at 3:34









IreneIrene

688612




688612








  • 1




    $begingroup$
    You want references for that? Set builder notation is $textbf{notation}$: i.e., if you want to use a different symbol, go for it.
    $endgroup$
    – Don Thousand
    Dec 14 '18 at 3:42






  • 2




    $begingroup$
    There are many cases where people use nonstandard notation. As long as it is established before hand that the people are using the same notation it is okay. Rather then "actual notation" it might be better to say "standard notation" or "most commonly used notation"
    $endgroup$
    – Q the Platypus
    Dec 14 '18 at 3:44










  • $begingroup$
    Thank you for your comments. I was serching for references that establishes the vertical line or colon as standard notation, and that gives some reason for not using "/" instead of the other ones. This notation is going to be use on a very elementary material for school students.
    $endgroup$
    – Irene
    Dec 14 '18 at 11:47






  • 1




    $begingroup$
    You could make up reasons why $/$ is a bad choice, but you could just as well make up such reasons for $:$ and $|$. The real reason is just that it's the notation that everyone else uses. In any case, it seems rather bizarre that you need a reference to "prove" this, especially if this is just for students.
    $endgroup$
    – Eric Wofsey
    Dec 15 '18 at 22:14










  • $begingroup$
    It never occurred to me that the ":" in the weirdly-named "set-builder" notation was the mathematical notation for "such that". I suppose, then, that "{" is the notation for "the set of all", but what does "}" stand for?
    $endgroup$
    – bof
    Dec 15 '18 at 23:56














  • 1




    $begingroup$
    You want references for that? Set builder notation is $textbf{notation}$: i.e., if you want to use a different symbol, go for it.
    $endgroup$
    – Don Thousand
    Dec 14 '18 at 3:42






  • 2




    $begingroup$
    There are many cases where people use nonstandard notation. As long as it is established before hand that the people are using the same notation it is okay. Rather then "actual notation" it might be better to say "standard notation" or "most commonly used notation"
    $endgroup$
    – Q the Platypus
    Dec 14 '18 at 3:44










  • $begingroup$
    Thank you for your comments. I was serching for references that establishes the vertical line or colon as standard notation, and that gives some reason for not using "/" instead of the other ones. This notation is going to be use on a very elementary material for school students.
    $endgroup$
    – Irene
    Dec 14 '18 at 11:47






  • 1




    $begingroup$
    You could make up reasons why $/$ is a bad choice, but you could just as well make up such reasons for $:$ and $|$. The real reason is just that it's the notation that everyone else uses. In any case, it seems rather bizarre that you need a reference to "prove" this, especially if this is just for students.
    $endgroup$
    – Eric Wofsey
    Dec 15 '18 at 22:14










  • $begingroup$
    It never occurred to me that the ":" in the weirdly-named "set-builder" notation was the mathematical notation for "such that". I suppose, then, that "{" is the notation for "the set of all", but what does "}" stand for?
    $endgroup$
    – bof
    Dec 15 '18 at 23:56








1




1




$begingroup$
You want references for that? Set builder notation is $textbf{notation}$: i.e., if you want to use a different symbol, go for it.
$endgroup$
– Don Thousand
Dec 14 '18 at 3:42




$begingroup$
You want references for that? Set builder notation is $textbf{notation}$: i.e., if you want to use a different symbol, go for it.
$endgroup$
– Don Thousand
Dec 14 '18 at 3:42




2




2




$begingroup$
There are many cases where people use nonstandard notation. As long as it is established before hand that the people are using the same notation it is okay. Rather then "actual notation" it might be better to say "standard notation" or "most commonly used notation"
$endgroup$
– Q the Platypus
Dec 14 '18 at 3:44




$begingroup$
There are many cases where people use nonstandard notation. As long as it is established before hand that the people are using the same notation it is okay. Rather then "actual notation" it might be better to say "standard notation" or "most commonly used notation"
$endgroup$
– Q the Platypus
Dec 14 '18 at 3:44












$begingroup$
Thank you for your comments. I was serching for references that establishes the vertical line or colon as standard notation, and that gives some reason for not using "/" instead of the other ones. This notation is going to be use on a very elementary material for school students.
$endgroup$
– Irene
Dec 14 '18 at 11:47




$begingroup$
Thank you for your comments. I was serching for references that establishes the vertical line or colon as standard notation, and that gives some reason for not using "/" instead of the other ones. This notation is going to be use on a very elementary material for school students.
$endgroup$
– Irene
Dec 14 '18 at 11:47




1




1




$begingroup$
You could make up reasons why $/$ is a bad choice, but you could just as well make up such reasons for $:$ and $|$. The real reason is just that it's the notation that everyone else uses. In any case, it seems rather bizarre that you need a reference to "prove" this, especially if this is just for students.
$endgroup$
– Eric Wofsey
Dec 15 '18 at 22:14




$begingroup$
You could make up reasons why $/$ is a bad choice, but you could just as well make up such reasons for $:$ and $|$. The real reason is just that it's the notation that everyone else uses. In any case, it seems rather bizarre that you need a reference to "prove" this, especially if this is just for students.
$endgroup$
– Eric Wofsey
Dec 15 '18 at 22:14












$begingroup$
It never occurred to me that the ":" in the weirdly-named "set-builder" notation was the mathematical notation for "such that". I suppose, then, that "{" is the notation for "the set of all", but what does "}" stand for?
$endgroup$
– bof
Dec 15 '18 at 23:56




$begingroup$
It never occurred to me that the ":" in the weirdly-named "set-builder" notation was the mathematical notation for "such that". I suppose, then, that "{" is the notation for "the set of all", but what does "}" stand for?
$endgroup$
– bof
Dec 15 '18 at 23:56










1 Answer
1






active

oldest

votes


















1












$begingroup$

Both $vert$ and $:$ are used.
$vert$ perhaps, being the most historical.

For clarity of notation, $:$ is preferred.

For example imagine using $vert$ in the definition of ${ x : |x| < 5 }$.



Though I don't know the source of the recent amateurish use of /, it is to be avoided since it is not accepted, causes confusion and lacks notational clarity. For example, ${ x/y / 1/xy < 10 }$.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
    $endgroup$
    – Irene
    Dec 14 '18 at 11:49













Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3038902%2fnotation-for-such-that-on-a-set-builder-notation%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

Both $vert$ and $:$ are used.
$vert$ perhaps, being the most historical.

For clarity of notation, $:$ is preferred.

For example imagine using $vert$ in the definition of ${ x : |x| < 5 }$.



Though I don't know the source of the recent amateurish use of /, it is to be avoided since it is not accepted, causes confusion and lacks notational clarity. For example, ${ x/y / 1/xy < 10 }$.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
    $endgroup$
    – Irene
    Dec 14 '18 at 11:49


















1












$begingroup$

Both $vert$ and $:$ are used.
$vert$ perhaps, being the most historical.

For clarity of notation, $:$ is preferred.

For example imagine using $vert$ in the definition of ${ x : |x| < 5 }$.



Though I don't know the source of the recent amateurish use of /, it is to be avoided since it is not accepted, causes confusion and lacks notational clarity. For example, ${ x/y / 1/xy < 10 }$.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
    $endgroup$
    – Irene
    Dec 14 '18 at 11:49
















1












1








1





$begingroup$

Both $vert$ and $:$ are used.
$vert$ perhaps, being the most historical.

For clarity of notation, $:$ is preferred.

For example imagine using $vert$ in the definition of ${ x : |x| < 5 }$.



Though I don't know the source of the recent amateurish use of /, it is to be avoided since it is not accepted, causes confusion and lacks notational clarity. For example, ${ x/y / 1/xy < 10 }$.






share|cite|improve this answer











$endgroup$



Both $vert$ and $:$ are used.
$vert$ perhaps, being the most historical.

For clarity of notation, $:$ is preferred.

For example imagine using $vert$ in the definition of ${ x : |x| < 5 }$.



Though I don't know the source of the recent amateurish use of /, it is to be avoided since it is not accepted, causes confusion and lacks notational clarity. For example, ${ x/y / 1/xy < 10 }$.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Dec 15 '18 at 23:45

























answered Dec 14 '18 at 8:52









William ElliotWilliam Elliot

8,0702720




8,0702720












  • $begingroup$
    Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
    $endgroup$
    – Irene
    Dec 14 '18 at 11:49




















  • $begingroup$
    Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
    $endgroup$
    – Irene
    Dec 14 '18 at 11:49


















$begingroup$
Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
$endgroup$
– Irene
Dec 14 '18 at 11:49






$begingroup$
Thank you very much, I know it is to be avoided for that reasons, but I was looking for some reference, if there was some. I found this link from Springer: link.springer.com/content/pdf/bbm%3A978-0-85729-829-4%2F1.pdf , do you think it can work as one?
$endgroup$
– Irene
Dec 14 '18 at 11:49




















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3038902%2fnotation-for-such-that-on-a-set-builder-notation%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Ellipse (mathématiques)

Image
Pour les articles homonymes, voir Ellipse. L'ellipse est le lieu des points dont la somme des distances à deux points fixes, dits foyers, est constante. Section du cône ou projection du cercle. En géométrie, une ellipse est une courbe plane fermée obtenue par l’intersection d’un cône de révolution avec un plan, à condition que celui-ci coupe l'axe de rotation du cône ou du cylindre : c'est une conique d'excentricité strictement comprise entre 0 et 1. On peut également la définir comme le lieu des points dont la somme des distances à deux points fixes, dits foyers, est constante (sa construction par la méthode du jardinier est très simple). Dans la vie courante, l’ellipse est la forme qu'on perçoit en regardant un cercle en perspective, ou la figure formée par l’ombre d'un disque sur une surface plane. On retrouve aussi, en première approximation [ 1 ] , des ellipses dans les trajectoires des corps célestes (planètes, comètes ou satellites arti...
Read more

Quarter-circle Tiles

Image
up vote 0 down vote favorite I have $99$ identical square tiles, each with a quarter-circle drawn on it like this: [asy] size(1.5cm); draw(Arc((2,0),1,90,180),red+1); draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)); [/asy] When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form? I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it. expected-value share | cite | improve this question asked Nov 20 at 15:03 6minecraftninja 1 2 ...
Read more

Mont Emei

Image
Mont Emei.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Vue du sommet Wanfo du mont Emei Géographie Altitude 3 099  m , Wanfo Coordonnées 29° 31′ 11″ nord, 103° 19′ 57″ est Administration Pays   Chine Province Sichuan Ville-préfecture Leshan Géolocalisation sur la carte : Sichuan Mont Emei Géolocalisation sur la carte : Chine Mont Emei modifier   Paysage panoramique du mont Emei, incluant le paysage panoramique du grand Bouddha de Leshan *   Patrimoine mondial de l'UNESCO Passerelle en bois sur le versant ouest Pays   Chine Subdivision Sichuan Type Mixte Critères (iv) (vi) (x) Superficie 15 400 ha Numéro d’identification 779 Zone géographique Asie et Pacifique  ** Année d’inscription 1996 (20 e session) * Descriptif officiel UNESCO ** Classification géog...
Read more