Build a bijection between $mathcal{P}(mathbb{Z}^+)$ and $mathcal{P} (mathbb{Z})$











up vote
0
down vote

favorite
1












I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?










share|cite|improve this question


















  • 2




    I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
    – Melody
    Nov 15 at 5:17















up vote
0
down vote

favorite
1












I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?










share|cite|improve this question


















  • 2




    I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
    – Melody
    Nov 15 at 5:17













up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?










share|cite|improve this question













I tried building a function out of the cardinality of the two, but I'm not sure if you can do that. Is there a better way of approaching the problem?







functions






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 15 at 5:13









Umuko

945




945








  • 2




    I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
    – Melody
    Nov 15 at 5:17














  • 2




    I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
    – Melody
    Nov 15 at 5:17








2




2




I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17




I would try and establish a bijection between $mathbb{Z}^+$ and $mathbb{Z}$. This would induce a bijection between their power sets. Suppose $f:mathbb{Z}^+tomathbb{Z}$ is bijective. Then we define $f^*:mathcal{P}(mathbb{Z}^+)tomathcal{P}(mathbb{Z})$ by $$f^*({z_1,z_2,...})={f(z_1),f(z_2),...}.$$
– Melody
Nov 15 at 5:17















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%2f2999248%2fbuild-a-bijection-between-mathcalp-mathbbz-and-mathcalp-mathbb%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



















































 


draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999248%2fbuild-a-bijection-between-mathcalp-mathbbz-and-mathcalp-mathbb%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

Актюбинская область

QoS: MAC-Priority for clients behind a repeater

AnyDesk - Fatal Program Failure