Notation of $d$-dimensional cuboids: $prod_{i = 1}^{d} [a_i, b_i] = times_{i = 1}^{d} [a_i, b_i]$?












1














When writing about axially parallel cuboids
begin{equation*}
Q := [a_i, b_i] times ldots times [a_d, b_d],
end{equation*}

where $a_i, b_i in mathbb{R}$ for all $i$ I often see those two notations and wonder why the first one is often used instead of the second:
begin{equation*}
prod_{i = 1}^{d} [a_i, b_i]
qquad text{and} qquad
times_{i = 1}^{d} [a_i, b_i]
end{equation*}










share|cite|improve this question






















  • I guess for the same reason $n!=prod_{i=1}^n i$ is preferred to $n!=times_{i=1}^n i$ and $frac{n(n+1)}2=sum_{i=0}^n i$ is preferred to $frac{n(n+1)}2=+_{i=0}^n i$ or to $bigoplus_{i=0}^n i$.
    – Saucy O'Path
    Dec 26 at 16:48












  • I'd prefer to use the second way of writing a Cartesian product, because the first way is sometimes used for set intersection instead of $bigcap$. I think there's no real reason behind it, other than the word "product", which implies some connection to multiplication
    – Jakobian
    Dec 26 at 17:04












  • @SaucyO'Path But I thought $$times_{j = 1}^{n} A_i = { (a_1, ldots, a_n): a_i in A_i forall i {1, ldots, n}}.$$How is that consistent with $n! = times_{j = 1}^{n} j$?
    – Viktor Glombik
    Dec 26 at 17:13


















1














When writing about axially parallel cuboids
begin{equation*}
Q := [a_i, b_i] times ldots times [a_d, b_d],
end{equation*}

where $a_i, b_i in mathbb{R}$ for all $i$ I often see those two notations and wonder why the first one is often used instead of the second:
begin{equation*}
prod_{i = 1}^{d} [a_i, b_i]
qquad text{and} qquad
times_{i = 1}^{d} [a_i, b_i]
end{equation*}










share|cite|improve this question






















  • I guess for the same reason $n!=prod_{i=1}^n i$ is preferred to $n!=times_{i=1}^n i$ and $frac{n(n+1)}2=sum_{i=0}^n i$ is preferred to $frac{n(n+1)}2=+_{i=0}^n i$ or to $bigoplus_{i=0}^n i$.
    – Saucy O'Path
    Dec 26 at 16:48












  • I'd prefer to use the second way of writing a Cartesian product, because the first way is sometimes used for set intersection instead of $bigcap$. I think there's no real reason behind it, other than the word "product", which implies some connection to multiplication
    – Jakobian
    Dec 26 at 17:04












  • @SaucyO'Path But I thought $$times_{j = 1}^{n} A_i = { (a_1, ldots, a_n): a_i in A_i forall i {1, ldots, n}}.$$How is that consistent with $n! = times_{j = 1}^{n} j$?
    – Viktor Glombik
    Dec 26 at 17:13
















1












1








1







When writing about axially parallel cuboids
begin{equation*}
Q := [a_i, b_i] times ldots times [a_d, b_d],
end{equation*}

where $a_i, b_i in mathbb{R}$ for all $i$ I often see those two notations and wonder why the first one is often used instead of the second:
begin{equation*}
prod_{i = 1}^{d} [a_i, b_i]
qquad text{and} qquad
times_{i = 1}^{d} [a_i, b_i]
end{equation*}










share|cite|improve this question













When writing about axially parallel cuboids
begin{equation*}
Q := [a_i, b_i] times ldots times [a_d, b_d],
end{equation*}

where $a_i, b_i in mathbb{R}$ for all $i$ I often see those two notations and wonder why the first one is often used instead of the second:
begin{equation*}
prod_{i = 1}^{d} [a_i, b_i]
qquad text{and} qquad
times_{i = 1}^{d} [a_i, b_i]
end{equation*}







notation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 26 at 16:45









Viktor Glombik

574425




574425












  • I guess for the same reason $n!=prod_{i=1}^n i$ is preferred to $n!=times_{i=1}^n i$ and $frac{n(n+1)}2=sum_{i=0}^n i$ is preferred to $frac{n(n+1)}2=+_{i=0}^n i$ or to $bigoplus_{i=0}^n i$.
    – Saucy O'Path
    Dec 26 at 16:48












  • I'd prefer to use the second way of writing a Cartesian product, because the first way is sometimes used for set intersection instead of $bigcap$. I think there's no real reason behind it, other than the word "product", which implies some connection to multiplication
    – Jakobian
    Dec 26 at 17:04












  • @SaucyO'Path But I thought $$times_{j = 1}^{n} A_i = { (a_1, ldots, a_n): a_i in A_i forall i {1, ldots, n}}.$$How is that consistent with $n! = times_{j = 1}^{n} j$?
    – Viktor Glombik
    Dec 26 at 17:13




















  • I guess for the same reason $n!=prod_{i=1}^n i$ is preferred to $n!=times_{i=1}^n i$ and $frac{n(n+1)}2=sum_{i=0}^n i$ is preferred to $frac{n(n+1)}2=+_{i=0}^n i$ or to $bigoplus_{i=0}^n i$.
    – Saucy O'Path
    Dec 26 at 16:48












  • I'd prefer to use the second way of writing a Cartesian product, because the first way is sometimes used for set intersection instead of $bigcap$. I think there's no real reason behind it, other than the word "product", which implies some connection to multiplication
    – Jakobian
    Dec 26 at 17:04












  • @SaucyO'Path But I thought $$times_{j = 1}^{n} A_i = { (a_1, ldots, a_n): a_i in A_i forall i {1, ldots, n}}.$$How is that consistent with $n! = times_{j = 1}^{n} j$?
    – Viktor Glombik
    Dec 26 at 17:13


















I guess for the same reason $n!=prod_{i=1}^n i$ is preferred to $n!=times_{i=1}^n i$ and $frac{n(n+1)}2=sum_{i=0}^n i$ is preferred to $frac{n(n+1)}2=+_{i=0}^n i$ or to $bigoplus_{i=0}^n i$.
– Saucy O'Path
Dec 26 at 16:48






I guess for the same reason $n!=prod_{i=1}^n i$ is preferred to $n!=times_{i=1}^n i$ and $frac{n(n+1)}2=sum_{i=0}^n i$ is preferred to $frac{n(n+1)}2=+_{i=0}^n i$ or to $bigoplus_{i=0}^n i$.
– Saucy O'Path
Dec 26 at 16:48














I'd prefer to use the second way of writing a Cartesian product, because the first way is sometimes used for set intersection instead of $bigcap$. I think there's no real reason behind it, other than the word "product", which implies some connection to multiplication
– Jakobian
Dec 26 at 17:04






I'd prefer to use the second way of writing a Cartesian product, because the first way is sometimes used for set intersection instead of $bigcap$. I think there's no real reason behind it, other than the word "product", which implies some connection to multiplication
– Jakobian
Dec 26 at 17:04














@SaucyO'Path But I thought $$times_{j = 1}^{n} A_i = { (a_1, ldots, a_n): a_i in A_i forall i {1, ldots, n}}.$$How is that consistent with $n! = times_{j = 1}^{n} j$?
– Viktor Glombik
Dec 26 at 17:13






@SaucyO'Path But I thought $$times_{j = 1}^{n} A_i = { (a_1, ldots, a_n): a_i in A_i forall i {1, ldots, n}}.$$How is that consistent with $n! = times_{j = 1}^{n} j$?
– Viktor Glombik
Dec 26 at 17:13

















active

oldest

votes











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%2f3053093%2fnotation-of-d-dimensional-cuboids-prod-i-1d-a-i-b-i-times-i%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes
















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.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • 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.


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%2f3053093%2fnotation-of-d-dimensional-cuboids-prod-i-1d-a-i-b-i-times-i%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

Human spaceflight

Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

張江高科駅