Reference request: Set of n-Multisets of elements in $mathbbN$ is countable setWhy does mathematical convention deal so ineptly with multisets?Is $cap_n=1^infty left( mathbbR setminus A_n right) $ countable set?Prove that there exists a countable collection of rectangles in $mathbbR^n$Multisets and cardinalityAlgorithm for generating the intersection of two multisetsIs there a name for the infinite sequence of k-multisets with one element, two elements, etc.?Can I use inclusion symbol to address a multiset's elements?Arranging $mathbb N$ into a two-dimensional array to prove a countably infinite collection of countable sets is countable.Category of Multisets and SpansProof for bijection between the set of k-multisets & the set of k-subsets.

Why is this plane circling around the Lucknow airport every day?

Who deserves to be first and second author? PhD student who collected data, research associate who wrote the paper or supervisor?

Do items de-spawn in Diablo?

Rejected in 4th interview round citing insufficient years of experience

What Happens when Passenger Refuses to Fly Boeing 737 Max?

Can you reject a postdoc offer after the PI has paid a large sum for flights/accommodation for your visit?

How do I locate a classical quotation?

Virginia employer terminated employee and wants signing bonus returned

infinitive telling the purpose

Why would one plane in this picture not have gear down yet?

Does splitting a potentially monolithic application into several smaller ones help prevent bugs?

Is it true that real estate prices mainly go up?

Does "variables should live in the smallest scope as possible" include the case "variables should not exist if possible"?

In the late 1940’s to early 1950’s what technology was available that could melt a LOT of ice?

Is there a window switcher for GNOME that shows the actual window?

Unreachable code, but reachable with exception

Aliens englobed the Solar System: will we notice?

Make a transparent 448*448 image

How much attack damage does the AC boost from a shield prevent on average?

What is the chance of making a successful appeal to dismissal decision from a PhD program after failing the qualifying exam in the 2nd attempt?

How could our ancestors have domesticated a solitary predator?

How do I deal with a powergamer in a game full of beginners in a school club?

Am I not good enough for you?

Finding algorithms of QGIS commands?



Reference request: Set of n-Multisets of elements in $mathbbN$ is countable set


Why does mathematical convention deal so ineptly with multisets?Is $cap_n=1^infty left( mathbbR setminus A_n right) $ countable set?Prove that there exists a countable collection of rectangles in $mathbbR^n$Multisets and cardinalityAlgorithm for generating the intersection of two multisetsIs there a name for the infinite sequence of k-multisets with one element, two elements, etc.?Can I use inclusion symbol to address a multiset's elements?Arranging $mathbb N$ into a two-dimensional array to prove a countably infinite collection of countable sets is countable.Category of Multisets and SpansProof for bijection between the set of k-multisets & the set of k-subsets.













0












$begingroup$


Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.






discrete-mathematics elementary-set-theory multisets







share|cite|improve this question











$endgroup$











  • $begingroup$
    There is a surjection from the finite sequences onto multisets.
    $endgroup$
    – Asaf Karagila♦
    2 days ago















0












$begingroup$


Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.






discrete-mathematics elementary-set-theory multisets







share|cite|improve this question











$endgroup$











  • $begingroup$
    There is a surjection from the finite sequences onto multisets.
    $endgroup$
    – Asaf Karagila♦
    2 days ago













0












0








0





$begingroup$


Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.






discrete-mathematics elementary-set-theory multisets







share|cite|improve this question











$endgroup$




Let $n in mathbbN$ be fixed. I need a reference for the statement, that the collection of multisets of length $n$ with elements in $mathbbN$
beginequation
M_mathbbN = a_i in mathbbN
endequation
is a set and is countable.






discrete-mathematics elementary-set-theory multisets




discrete-mathematics elementary-set-theory multisets






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Asaf Karagila♦

306k33438769




306k33438769










asked 2 days ago









warpfelwarpfel

1067




1067











  • $begingroup$
    There is a surjection from the finite sequences onto multisets.
    $endgroup$
    – Asaf Karagila♦
    2 days ago
















  • $begingroup$
    There is a surjection from the finite sequences onto multisets.
    $endgroup$
    – Asaf Karagila♦
    2 days ago















$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago




$begingroup$
There is a surjection from the finite sequences onto multisets.
$endgroup$
– Asaf Karagila♦
2 days ago










1 Answer
1






active

oldest

votes


















0












$begingroup$

There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.






share|cite|improve this answer









$endgroup$












    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%2f3142204%2freference-request-set-of-n-multisets-of-elements-in-mathbbn-is-countable-s%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









    0












    $begingroup$

    There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.






    share|cite|improve this answer









    $endgroup$

















      0












      $begingroup$

      There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.






      share|cite|improve this answer









      $endgroup$















        0












        0








        0





        $begingroup$

        There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.






        share|cite|improve this answer









        $endgroup$



        There is a bijection $mathcalM_mathbbN rightarrow bigcup_k=0^inftymathbbN^k$. Now each $mathbbN^k$ is countable and countable unions of countable sets are again countable.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 2 days ago









        An_876_JokeAn_876_Joke

        1036




        1036



























            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%2f3142204%2freference-request-set-of-n-multisets-of-elements-in-mathbbn-is-countable-s%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

            Moe incest case Sentencing See also References Navigation menu"'Australian Josef Fritzl' fathered four children by daughter""Small town recoils in horror at 'Australian Fritzl' incest case""Victorian rape allegations echo Fritzl case - Just In (Australian Broadcasting Corporation)""Incest father jailed for 22 years""'Australian Fritzl' sentenced to 22 years in prison for abusing daughter for three decades""RSJ v The Queen"

            2009 crimes in AustraliaPeople convicted of incestRape in AustraliaChild abuse incidents and cases Victoria Police Moe, Victoria, Australiarapedphysically abusedviolencediedallegationsNews LimitedinvestigateMelbournedevelopmental problemsintellectually disabledspeech impedimentbirth certificateschargedsexual abuseDNA testspleadedguiltyincestindecent assaultcommon assaultsentencingimprisonmentparolesex offender registryappeal The Moe incest case emerged in February 2007 when a woman, identified as M for legal reasons, reported to Victoria Police in the town of Moe, Victoria, Australia that her 63-year-old father, RSJ, had raped, [1] [2] physically abused, and kept her a virtual prisoner in her own home between 1977 and 2005. Police had known about the alleged abuse since 2005, when M first came forward, but could not act because she did not want to cooperate after her father threatened violence against her mother and siblings. The J family had been known to authorities for more than ...
            Read more

            John Burke, 9th Earl of Clanricarde References Navigation menuA General and heraldic dictionary of the peerage and baronetage of the British EmpireLeigh Rayment's Peerage Pages

            People from County GalwayJacobite military personnel of the Williamite War in IrelandHouse of Burke1642 births1722 deathsMembers of the Irish House of LordsEarls of ClanricardePeers of Ireland created by James II IrishpeerWilliam Burke, 7th Earl of ClanricardeRichardisle of InishbofinWilliamite War in IrelandBattle of AughrimUlick Burke, 1st Viscount GalwayProtestantsprivate act of the English ParliamentCatholicWild GeeseSpainBolognaFontenoyHonora BurkePatrick Sarsfield, 1st Earl of Lucan John Burke, 9th Earl of Clanricarde (1642–1722) was an Irish peer. Burke was a younger son of William Burke, 7th Earl of Clanricarde and succeeded his brother Richard. He was created Baron Bophin (over the isle of Inishbofin where Burke is still a common surname amongst the islanders [1] ) in 1689 and commanded a foot regiment as its colonel during the Williamite War in Ireland. He was taken prisoner at the Battle of Aughrim in 1691 and outlawed. His younger brother Ulick Burke, 1st Viscount G...
            Read more

            Football at the 1986 Brunei Merdeka Games Contents Teams Group stage Knockout stage References Navigation menu"Brunei Merdeka Games 1986".

            Image
            1986 in Asian footballFootball at the Brunei Merdeka Games1986 in Brunei1986 in Singaporean football1986 in Malaysian football1986 in Thai sport Bandar Seri BegawanBruneiMalaysia Cup Football at the 1986 Brunei Merdeka Games Tournament details Host country Brunei Dates 19 July – 27 July Teams 10 Final positions Champions Persib Bandung (1st title) Runners-up Malaysia B Third place   Brunei Fourth place Singapore XI Tournament statistics Matches played 10 Goals scored 25 (2.5 per match) ← 1985 1987 → The football tournament at the 1986 Brunei Merdeka Games was held from July 19 to 27 in Bandar Seri Begawan, Brunei. The tournament was also referred to as the Sultan Hassanal Bolkiah Cup, or the second Brunei Pesta Sukan Cup. Contents 1 Teams 2 Group stage 2.1 Group A 2.2 Group B 3 Knockout stage 3.1 Semi-finals 3.2 Bronze medal match 3.3 Gold medal match 4 References Teams It is likely that the Philippines team was the full national team, bu...
            Read more