Find all 8 elements of order 3 in $mathbb{R}^2/mathbb{Z}^2$











up vote
0
down vote

favorite












What does the notation $mathbb{R}^2/mathbb{Z}^2$ actually mean? Is it $(x_1,x_2)$?










share|cite|improve this question






















  • It means pairs of real numbers, but only up to shifts by integers. For example, $(1.1, 5.6) = (0.1, 0.6) = (-0.9, 100.6)$.
    – Joppy
    Nov 23 at 2:07










  • ohhh okk thxxxx
    – m.bazza
    Nov 23 at 2:12










  • ahh i got it now thx
    – m.bazza
    Nov 23 at 2:15










  • Also, check out the guide for new askers.
    – Jyrki Lahtonen
    Nov 23 at 3:54










  • Additively or multiplicatively?
    – Wuestenfux
    Nov 23 at 15:10















up vote
0
down vote

favorite












What does the notation $mathbb{R}^2/mathbb{Z}^2$ actually mean? Is it $(x_1,x_2)$?










share|cite|improve this question






















  • It means pairs of real numbers, but only up to shifts by integers. For example, $(1.1, 5.6) = (0.1, 0.6) = (-0.9, 100.6)$.
    – Joppy
    Nov 23 at 2:07










  • ohhh okk thxxxx
    – m.bazza
    Nov 23 at 2:12










  • ahh i got it now thx
    – m.bazza
    Nov 23 at 2:15










  • Also, check out the guide for new askers.
    – Jyrki Lahtonen
    Nov 23 at 3:54










  • Additively or multiplicatively?
    – Wuestenfux
    Nov 23 at 15:10













up vote
0
down vote

favorite









up vote
0
down vote

favorite











What does the notation $mathbb{R}^2/mathbb{Z}^2$ actually mean? Is it $(x_1,x_2)$?










share|cite|improve this question













What does the notation $mathbb{R}^2/mathbb{Z}^2$ actually mean? Is it $(x_1,x_2)$?







abstract-algebra






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 23 at 2:05









m.bazza

827




827












  • It means pairs of real numbers, but only up to shifts by integers. For example, $(1.1, 5.6) = (0.1, 0.6) = (-0.9, 100.6)$.
    – Joppy
    Nov 23 at 2:07










  • ohhh okk thxxxx
    – m.bazza
    Nov 23 at 2:12










  • ahh i got it now thx
    – m.bazza
    Nov 23 at 2:15










  • Also, check out the guide for new askers.
    – Jyrki Lahtonen
    Nov 23 at 3:54










  • Additively or multiplicatively?
    – Wuestenfux
    Nov 23 at 15:10


















  • It means pairs of real numbers, but only up to shifts by integers. For example, $(1.1, 5.6) = (0.1, 0.6) = (-0.9, 100.6)$.
    – Joppy
    Nov 23 at 2:07










  • ohhh okk thxxxx
    – m.bazza
    Nov 23 at 2:12










  • ahh i got it now thx
    – m.bazza
    Nov 23 at 2:15










  • Also, check out the guide for new askers.
    – Jyrki Lahtonen
    Nov 23 at 3:54










  • Additively or multiplicatively?
    – Wuestenfux
    Nov 23 at 15:10
















It means pairs of real numbers, but only up to shifts by integers. For example, $(1.1, 5.6) = (0.1, 0.6) = (-0.9, 100.6)$.
– Joppy
Nov 23 at 2:07




It means pairs of real numbers, but only up to shifts by integers. For example, $(1.1, 5.6) = (0.1, 0.6) = (-0.9, 100.6)$.
– Joppy
Nov 23 at 2:07












ohhh okk thxxxx
– m.bazza
Nov 23 at 2:12




ohhh okk thxxxx
– m.bazza
Nov 23 at 2:12












ahh i got it now thx
– m.bazza
Nov 23 at 2:15




ahh i got it now thx
– m.bazza
Nov 23 at 2:15












Also, check out the guide for new askers.
– Jyrki Lahtonen
Nov 23 at 3:54




Also, check out the guide for new askers.
– Jyrki Lahtonen
Nov 23 at 3:54












Additively or multiplicatively?
– Wuestenfux
Nov 23 at 15:10




Additively or multiplicatively?
– Wuestenfux
Nov 23 at 15:10















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',
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%2f3009893%2ffind-all-8-elements-of-order-3-in-mathbbr2-mathbbz2%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%2f3009893%2ffind-all-8-elements-of-order-3-in-mathbbr2-mathbbz2%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

Wiesbaden

Marschland

Dieringhausen