Find function $f:[0,1]to mathbb R$, whose set of discontinuities is such that $left{ frac{k}{2^n}; quad k,n...












1














Find function $fcolon[0,1]to mathbb R$, whose set of discontinuities is such that



$$left{frac{k}{2^n}; quad k,n in mathbb N, k le 2^nright }$$



I guess that it is Riemann function or something like that but I have no clue how it would look like






real-analysis continuity







share|cite|improve this question
























  • The set of discontinuities is dense in $[0,1]$. So I think that it might be like Weierstrass function.
    – toric_actions
    2 days ago
















1














Find function $fcolon[0,1]to mathbb R$, whose set of discontinuities is such that



$$left{frac{k}{2^n}; quad k,n in mathbb N, k le 2^nright }$$



I guess that it is Riemann function or something like that but I have no clue how it would look like






real-analysis continuity







share|cite|improve this question
























  • The set of discontinuities is dense in $[0,1]$. So I think that it might be like Weierstrass function.
    – toric_actions
    2 days ago














1












1








1







Find function $fcolon[0,1]to mathbb R$, whose set of discontinuities is such that



$$left{frac{k}{2^n}; quad k,n in mathbb N, k le 2^nright }$$



I guess that it is Riemann function or something like that but I have no clue how it would look like






real-analysis continuity







share|cite|improve this question















Find function $fcolon[0,1]to mathbb R$, whose set of discontinuities is such that



$$left{frac{k}{2^n}; quad k,n in mathbb N, k le 2^nright }$$



I guess that it is Riemann function or something like that but I have no clue how it would look like






real-analysis continuity




real-analysis continuity






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Shaun

8,810113680




8,810113680










asked 2 days ago









math.trouble

566




566












  • The set of discontinuities is dense in $[0,1]$. So I think that it might be like Weierstrass function.
    – toric_actions
    2 days ago


















  • The set of discontinuities is dense in $[0,1]$. So I think that it might be like Weierstrass function.
    – toric_actions
    2 days ago
















The set of discontinuities is dense in $[0,1]$. So I think that it might be like Weierstrass function.
– toric_actions
2 days ago




The set of discontinuities is dense in $[0,1]$. So I think that it might be like Weierstrass function.
– toric_actions
2 days ago










1 Answer
1






active

oldest

votes


















5














Let $f(x) = 0$ whenever $x$ is not a dyadic fraction, and $fleft(frac{k}{2^n}right) = 2^{-n}$.






share|cite|improve this answer

















  • 2




    Might help to recognize that this is a modified Thomae's function.
    – Robert Wolfe
    2 days ago











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%2f3060890%2ffind-function-f0-1-to-mathbb-r-whose-set-of-discontinuities-is-such-that%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









5














Let $f(x) = 0$ whenever $x$ is not a dyadic fraction, and $fleft(frac{k}{2^n}right) = 2^{-n}$.






share|cite|improve this answer

















  • 2




    Might help to recognize that this is a modified Thomae's function.
    – Robert Wolfe
    2 days ago
















5














Let $f(x) = 0$ whenever $x$ is not a dyadic fraction, and $fleft(frac{k}{2^n}right) = 2^{-n}$.






share|cite|improve this answer

















  • 2




    Might help to recognize that this is a modified Thomae's function.
    – Robert Wolfe
    2 days ago














5












5








5






Let $f(x) = 0$ whenever $x$ is not a dyadic fraction, and $fleft(frac{k}{2^n}right) = 2^{-n}$.






share|cite|improve this answer












Let $f(x) = 0$ whenever $x$ is not a dyadic fraction, and $fleft(frac{k}{2^n}right) = 2^{-n}$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 2 days ago









MathematicsStudent1122

8,52122366




8,52122366








  • 2




    Might help to recognize that this is a modified Thomae's function.
    – Robert Wolfe
    2 days ago














  • 2




    Might help to recognize that this is a modified Thomae's function.
    – Robert Wolfe
    2 days ago








2




2




Might help to recognize that this is a modified Thomae's function.
– Robert Wolfe
2 days ago




Might help to recognize that this is a modified Thomae's function.
– Robert Wolfe
2 days ago


















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%2f3060890%2ffind-function-f0-1-to-mathbb-r-whose-set-of-discontinuities-is-such-that%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

1300-talet

Image
Den här artikeln handlar om hundraårsperioden 1300–1399. För decenniet 1300–1309, se 1300-talet (decennium). .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output ...
Read more

1300-talet

Image
Den här artikeln handlar om hundraårsperioden 1300–1399. För decenniet 1300–1309, se 1300-talet (decennium). .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output ...
Read more

Display a custom attribute below product name in the front-end Magento 1.9.3.8

Image
0 I need to display a custom attribute bellow the product name and I don't know how can I call this attribute. I am editing the file /app/design/frontend/templatemela/MAG100219_1/template/catalog/product/view.phtml But how can I call this attribute in php? I tried calling a string echo with the name I put in the attribute, but it didn't work. Code is as below: <div class="page-title product-title"> <h1><?php echo $_helper->productAttribute($_product, $_product->getName(), 'name') ?></h1> </div> <div class="codigoinmetro"> <h2><?php echo $_helper->productAttribute($_product, $_product->getName(), 'registroinmetro') ?></h2> </div> php attrib...
Read more