Is it possible to multiply a set by a natural number?
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
edited 45 mins ago
clathratus
3,320331
asked 1 hour ago
Hunter KimuraHunter Kimura
211
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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
edited 45 mins ago
clathratus
3,320331
asked 1 hour ago
Hunter KimuraHunter Kimura
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.
2
Yes you could just define $$n{a_i}={na_i}$$
– clathratus
45 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
34 mins ago
add a comment |
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
edited 45 mins ago
clathratus
3,320331
asked 1 hour ago
Hunter KimuraHunter Kimura
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.
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
edited 45 mins ago
clathratus
3,320331
asked 1 hour ago
Hunter KimuraHunter Kimura
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.
edited 45 mins ago
clathratus
3,320331
asked 1 hour ago
Hunter KimuraHunter Kimura
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.
edited 45 mins ago
clathratus
3,320331
edited 45 mins ago
clathratus
3,320331
edited 45 mins ago
clathratus
3,320331
3,320331
asked 1 hour ago
Hunter KimuraHunter Kimura
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.
asked 1 hour ago
Hunter KimuraHunter Kimura
211
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
45 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
34 mins ago
add a comment |
2
Yes you could just define $$n{a_i}={na_i}$$
– clathratus
45 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
34 mins ago
2
2
Yes you could just define $$n{a_i}={na_i}$$
– clathratus
45 mins ago
Yes you could just define $$n{a_i}={na_i}$$
– clathratus
45 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
34 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
34 mins ago
add a comment |
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 $Bbb Z={dots,-2,-1,0,1,2,dots}$.
answered 1 hour ago
John DoeJohn Doe
10.7k11237
add a comment |
Yes..you have already defined the operation..a scalar multiplication on a set.
answered 1 hour ago
ershersh
19510
add a comment |
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2 Answers
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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 $Bbb Z={dots,-2,-1,0,1,2,dots}$.
answered 1 hour ago
John DoeJohn Doe
10.7k11237
add a comment |
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 $Bbb Z={dots,-2,-1,0,1,2,dots}$.
answered 1 hour ago
John DoeJohn Doe
10.7k11237
add a comment |
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 $Bbb Z={dots,-2,-1,0,1,2,dots}$.
answered 1 hour ago
John DoeJohn Doe
10.7k11237
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 $Bbb Z={dots,-2,-1,0,1,2,dots}$.
answered 1 hour ago
John DoeJohn Doe
10.7k11237
answered 1 hour ago
John DoeJohn Doe
10.7k11237
answered 1 hour ago
John DoeJohn Doe
10.7k11237
answered 1 hour ago
John DoeJohn Doe
10.7k11237
10.7k11237
add a comment |
add a comment |
Yes..you have already defined the operation..a scalar multiplication on a set.
answered 1 hour ago
ershersh
19510
add a comment |
Yes..you have already defined the operation..a scalar multiplication on a set.
answered 1 hour ago
ershersh
19510
add a comment |
Yes..you have already defined the operation..a scalar multiplication on a set.
answered 1 hour ago
ershersh
19510
Yes..you have already defined the operation..a scalar multiplication on a set.
answered 1 hour ago
ershersh
19510
answered 1 hour ago
ershersh
19510
answered 1 hour ago
ershersh
19510
answered 1 hour ago
ershersh
19510
19510
add a comment |
add a comment |
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.
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2
Yes you could just define $$n{a_i}={na_i}$$
– clathratus
45 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
34 mins ago