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







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  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    1 hour 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
    1 hour 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
    1 hour 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
    1 hour 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




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edited 1 hour ago









clathratus

3,320331




3,320331






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asked 2 hours ago









Hunter KimuraHunter Kimura

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Hunter Kimura is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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
    1 hour 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
    1 hour ago














  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    1 hour 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
    1 hour ago








2




2




Yes you could just define $$n{a_i}={na_i}$$
– clathratus
1 hour ago




Yes you could just define $$n{a_i}={na_i}$$
– clathratus
1 hour 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
1 hour 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
1 hour ago










2 Answers
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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





















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      2 Answers
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      2 Answers
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      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 1 hour 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






















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