Is it possible to multiply a set by a natural number?












4














Say I have a set $S={1, 4, 10, 7}$. Could I then multiply $S$ by $3$? Would that then look like $3S={3, 12, 30, 21}$? Any help would be really appreciated.






discrete-mathematics elementary-set-theory







share|cite|improve this question









New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    38 mins ago






  • 2




    You can certainly take a set of numbers $S= {1,4,10,7}$ and say "Hey, I'm going to multiply every element by $3$ and get the set ${3,12,20,21}$ and I'm going to call that set $3S$". And you can say "I'm going to refer to that as multiplying a set by a number, any objections? No? Good."
    – fleablood
    27 mins ago
















4














Say I have a set $S={1, 4, 10, 7}$. Could I then multiply $S$ by $3$? Would that then look like $3S={3, 12, 30, 21}$? Any help would be really appreciated.






discrete-mathematics elementary-set-theory







share|cite|improve this question









New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    38 mins ago






  • 2




    You can certainly take a set of numbers $S= {1,4,10,7}$ and say "Hey, I'm going to multiply every element by $3$ and get the set ${3,12,20,21}$ and I'm going to call that set $3S$". And you can say "I'm going to refer to that as multiplying a set by a number, any objections? No? Good."
    – fleablood
    27 mins ago














4












4








4







Say I have a set $S={1, 4, 10, 7}$. Could I then multiply $S$ by $3$? Would that then look like $3S={3, 12, 30, 21}$? Any help would be really appreciated.






discrete-mathematics elementary-set-theory







share|cite|improve this question









New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Say I have a set $S={1, 4, 10, 7}$. Could I then multiply $S$ by $3$? Would that then look like $3S={3, 12, 30, 21}$? Any help would be really appreciated.






discrete-mathematics elementary-set-theory




discrete-mathematics elementary-set-theory






share|cite|improve this question









New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 37 mins ago









clathratus

3,320331




3,320331






New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 1 hour ago









Hunter KimuraHunter Kimura

211




211




New contributor




Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    38 mins ago






  • 2




    You can certainly take a set of numbers $S= {1,4,10,7}$ and say "Hey, I'm going to multiply every element by $3$ and get the set ${3,12,20,21}$ and I'm going to call that set $3S$". And you can say "I'm going to refer to that as multiplying a set by a number, any objections? No? Good."
    – fleablood
    27 mins ago














  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    38 mins ago






  • 2




    You can certainly take a set of numbers $S= {1,4,10,7}$ and say "Hey, I'm going to multiply every element by $3$ and get the set ${3,12,20,21}$ and I'm going to call that set $3S$". And you can say "I'm going to refer to that as multiplying a set by a number, any objections? No? Good."
    – fleablood
    27 mins ago








2




2




Yes you could just define $$n{a_i}={na_i}$$
– clathratus
38 mins ago




Yes you could just define $$n{a_i}={na_i}$$
– clathratus
38 mins ago




2




2




You can certainly take a set of numbers $S= {1,4,10,7}$ and say "Hey, I'm going to multiply every element by $3$ and get the set ${3,12,20,21}$ and I'm going to call that set $3S$". And you can say "I'm going to refer to that as multiplying a set by a number, any objections? No? Good."
– fleablood
27 mins ago




You can certainly take a set of numbers $S= {1,4,10,7}$ and say "Hey, I'm going to multiply every element by $3$ and get the set ${3,12,20,21}$ and I'm going to call that set $3S$". And you can say "I'm going to refer to that as multiplying a set by a number, any objections? No? Good."
– fleablood
27 mins ago










2 Answers
2






active

oldest

votes


















5














Sure, we sometimes for example denote the set of even integers by $2Bbb Z={dots,-4,-2,0,2,4,dots}$, while the set of integers is $Bbb Z={dots,-2,-1,0,1,2,dots}$.






share|cite|improve this answer





























    3














    Yes..you have already defined the operation..a scalar multiplication on a set.






    share|cite|improve this answer





















      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
      });


      }
      });






      Hunter Kimura is a new contributor. Be nice, and check out our Code of Conduct.










      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3065819%2fis-it-possible-to-multiply-a-set-by-a-natural-number%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      5














      Sure, we sometimes for example denote the set of even integers by $2Bbb Z={dots,-4,-2,0,2,4,dots}$, while the set of integers is $Bbb Z={dots,-2,-1,0,1,2,dots}$.






      share|cite|improve this answer


























        5














        Sure, we sometimes for example denote the set of even integers by $2Bbb Z={dots,-4,-2,0,2,4,dots}$, while the set of integers is $Bbb Z={dots,-2,-1,0,1,2,dots}$.






        share|cite|improve this answer
























          5












          5








          5






          Sure, we sometimes for example denote the set of even integers by $2Bbb Z={dots,-4,-2,0,2,4,dots}$, while the set of integers is $Bbb Z={dots,-2,-1,0,1,2,dots}$.






          share|cite|improve this answer












          Sure, we sometimes for example denote the set of even integers by $2Bbb Z={dots,-4,-2,0,2,4,dots}$, while the set of integers is $Bbb Z={dots,-2,-1,0,1,2,dots}$.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 59 mins ago









          John DoeJohn Doe

          10.7k11237




          10.7k11237























              3














              Yes..you have already defined the operation..a scalar multiplication on a set.






              share|cite|improve this answer


























                3














                Yes..you have already defined the operation..a scalar multiplication on a set.






                share|cite|improve this answer
























                  3












                  3








                  3






                  Yes..you have already defined the operation..a scalar multiplication on a set.






                  share|cite|improve this answer












                  Yes..you have already defined the operation..a scalar multiplication on a set.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 1 hour ago









                  ershersh

                  19510




                  19510






















                      Hunter Kimura is a new contributor. Be nice, and check out our Code of Conduct.










                      draft saved

                      draft discarded


















                      Hunter Kimura is a new contributor. Be nice, and check out our Code of Conduct.













                      Hunter Kimura is a new contributor. Be nice, and check out our Code of Conduct.












                      Hunter Kimura is a new contributor. Be nice, and check out our Code of Conduct.
















                      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%2f3065819%2fis-it-possible-to-multiply-a-set-by-a-natural-number%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

                      サソリ

                      Image
                      この記事は検証可能な参考文献や出典が全く示されていないか、不十分です。 出典を追加して記事の信頼性向上にご協力ください。 （ 2019年1月 ） 「 サソリ 」のその他の用法については「サソリ (曖昧さ回避)」をご覧ください。 「 スコーピオン 」と「 スコルピオン 」はこの項目へ転送されています。その他の用法については「スコーピオン」をご覧ください。 サソリ目 生息年代: 430–0 Ma PreЄ Є O S D C P T J K Pg N シルル紀前期-現世 ダイオウサソリ（ Pandinus Imperator ） 分類 界 : 動物界 Animalia 門 : 節足動物門 Arthropoda 亜門 : 鋏角亜門 Chelicerata 綱 : クモガタ綱 Arachnida 目 : サソリ目 Scorpiones 学名 Scorpiones C. L. Koch, 1837 英名 Scorpion 上科 Pseudochactoidea キョクトウサソリ上科 Buthoidea Chaeriloidea Chactoidea Iuroidea Scorpionoidea サソリ （ サソリ類 、 蠍 、 蝎 、 scorpion ）は、鋏角亜門・クモガタ綱の サソリ目 （ Scorpiones ）に属する節足動物の総称である。体の前端に鋏型の触肢、後端に毒針を有する捕食者である。 1700種以上を含め、最古の化石記録は4億3千万年前のシルル紀まで遡る。有毒生物として広く知られるが、人間の命にかかわる毒を持つものはごく一部の種類に過ぎない。 目次 1 形態 1.1 前体 1.2 後体 1.2.1 中体 1.2.2 終体 2 雌雄 3 生態 3.1 天敵 3.2 生殖 4 分布 5 毒 6 蛍光現象 7 分類
                      Read more

                      広島県道265号伴広島線

                      Image
                      一般県道 広島県道265号伴広島線 路線延長 km 起点 広島県広島市安佐南区伴東7丁目 終点 広島県広島市中区榎町 接続する 主な道路 （記法） 広島県道38号広島豊平線 広島県道71号広島湯来線 山陽自動車道五日市IC 国道183号（ 国道261号重複） ■テンプレート（■ノート ■使い方） ■PJ道路 広島県道265号伴広島線 （ひろしまけんどう265ごう ともひろしません）は広島県広島市安佐南区から広島県広島市中区を結ぶ一般県道である。 目次 1 路線データ 2 通過する自治体 3 見どころ 4 接続道路 4.1 本線 4.2 旧道 5 別名 6 関連項目 路線データ 本線 起点：広島市安佐南区伴東7丁目・大原下橋南詰交差点（広島県道38号広島豊平線（本線・旧道）交点） 終点：広島市中区榎町・十日市交差点（国道183号（国道261号重用）交点） 総延長： 旧道 起点：広島市安佐南区伴東4丁目・新細坂交差点（広島県道38号広島豊平線交点） 終点：広島市安佐南区伴中央4丁目・寺組橋(南)交差点（広島県道265号伴広島線（本線）交点） 総延長： 通過する自治体 広島県 広島市（安佐南区、佐伯区、西区、中区） 見どころ 広島高速交通広島新交通1号線（アストラムライン） 広島広域公園 広島広域公園陸上競技場（広島ビッグアーチ） 己斐峠 己斐橋（太田川放水路） 天満橋（天満川） 接続道路 本線 広島県道38号広島豊平線（本線・旧道）（広島市安佐南区伴東7丁目・大原下橋南詰交差点〔起点〕） 広島県道71号広島湯来線（本線）（広島市安佐南区伴中央2丁目・伴交番入口交差点 - 広島市安佐南区伴中央4丁目・寺組橋(南)交差点間で重用） 広島県道71号広島湯来線（旧道）（広島県道265号伴広島線（旧道）重用）（広島市安佐南区伴中央4丁目・寺組橋(南)交差点） 広島県道71号広島湯来線（広島市安佐南区伴中央4丁目・寺組橋(南)交差点 - 広島市佐伯区五日市町石内・五月が丘(南)交差点間で重用）
                      Read more

                      Accessing regular linux commands in Huawei's Dopra Linux

                      Image
                      4 Backstory: I have a Huawei HG8245 router in my house and I want to change the default username/password. I've tried following this guide but the config file always gets reset. My ISP isn't helping either so I'm looking for other ways to accomplish this. The router has telnet access so this seems like a way to change the credentials. The first shell I gain access to looks like this: WAP> Pressing "?" gives me a list of available commands which I've pasted here, the two interesting ones are "su" and "shell". I can't seem to get su access, even after logging in as root (challenge password prompt, and then nothing happens), but shell gives me a proper linux shell. WAP>shell BusyBox v1.18.4 (2017-12-26 17:06:34 CST) built-in shell (ash) Enter 'hel
                      Read more