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
    2 hours ago






  • 3




    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
    2 hours ago










  • I'm not sure what is being asked here. You can most certainly do anything you want in maths (assuming logically valid). Are you asking about usefulness of this construction?
    – freakish
    7 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
    2 hours ago






  • 3




    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
    2 hours ago










  • I'm not sure what is being asked here. You can most certainly do anything you want in maths (assuming logically valid). Are you asking about usefulness of this construction?
    – freakish
    7 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









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edited 2 hours ago









clathratus

3,330331




3,330331






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asked 2 hours ago









Hunter KimuraHunter Kimura

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  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    2 hours ago






  • 3




    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
    2 hours ago










  • I'm not sure what is being asked here. You can most certainly do anything you want in maths (assuming logically valid). Are you asking about usefulness of this construction?
    – freakish
    7 mins ago
















  • 2




    Yes you could just define $$n{a_i}={na_i}$$
    – clathratus
    2 hours ago






  • 3




    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
    2 hours ago










  • I'm not sure what is being asked here. You can most certainly do anything you want in maths (assuming logically valid). Are you asking about usefulness of this construction?
    – freakish
    7 mins ago










2




2




Yes you could just define $$n{a_i}={na_i}$$
– clathratus
2 hours ago




Yes you could just define $$n{a_i}={na_i}$$
– clathratus
2 hours ago




3




3




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
2 hours 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
2 hours ago












I'm not sure what is being asked here. You can most certainly do anything you want in maths (assuming logically valid). Are you asking about usefulness of this construction?
– freakish
7 mins ago






I'm not sure what is being asked here. You can most certainly do anything you want in maths (assuming logically valid). Are you asking about usefulness of this construction?
– freakish
7 mins ago












2 Answers
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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 $Bbb Z={dots,-2,-1,0,1,2,dots}$.






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    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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      6














      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


























        6














        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
























          6












          6








          6






          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 2 hours 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 2 hours ago









                  ershersh

                  19510




                  19510






















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