Mixing
Set builder notation for pairs?
Clash Royale CLAN TAG#URR8PPP
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I have a set $S$ of integers. I want to select the element pairs $(i,j)$ of it such that $i=2*j$ and order of elements does not matter. How can I show it with the set builder notation ?
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
elementary-set-theory notation
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
asked Aug 6 at 22:31
xaki
31
 |Â
show 3 more comments
up vote
0
down vote
favorite
I have a set $S$ of integers. I want to select the element pairs $(i,j)$ of it such that $i=2*j$ and order of elements does not matter. How can I show it with the set builder notation ?
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
elementary-set-theory notation
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
asked Aug 6 at 22:31
xaki
31
1
Why not simply $$(2i,i) mid i in S$$?
– Clement C.
Aug 6 at 22:32
@ClementC. What if $2inotin S$
– Rushabh Mehta
Aug 6 at 22:33
@RushabhMehta Good point. Then it's a bit less nice, indeed: $$(2i,i) mid i in Scap S^2$$
– Clement C.
Aug 6 at 22:34
More, that both are in the set S: $~(2j,j): jin S, 2jin S$
– Graham Kemp
Aug 6 at 22:34
@ClementC. I wouldn't really call that set builder notation
– Rushabh Mehta
Aug 6 at 22:34
 |Â
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have a set $S$ of integers. I want to select the element pairs $(i,j)$ of it such that $i=2*j$ and order of elements does not matter. How can I show it with the set builder notation ?
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
elementary-set-theory notation
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
asked Aug 6 at 22:31
xaki
31
I have a set $S$ of integers. I want to select the element pairs $(i,j)$ of it such that $i=2*j$ and order of elements does not matter. How can I show it with the set builder notation ?
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
elementary-set-theory notation
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
asked Aug 6 at 22:31
xaki
31
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
edited Aug 6 at 23:01
Andrés E. Caicedo
63.2k7151236
63.2k7151236
asked Aug 6 at 22:31
xaki
31
asked Aug 6 at 22:31
xaki
31
asked Aug 6 at 22:31
xaki
31
31
1
Why not simply $$(2i,i) mid i in S$$?
– Clement C.
Aug 6 at 22:32
@ClementC. What if $2inotin S$
– Rushabh Mehta
Aug 6 at 22:33
@RushabhMehta Good point. Then it's a bit less nice, indeed: $$(2i,i) mid i in Scap S^2$$
– Clement C.
Aug 6 at 22:34
More, that both are in the set S: $~(2j,j): jin S, 2jin S$
– Graham Kemp
Aug 6 at 22:34
@ClementC. I wouldn't really call that set builder notation
– Rushabh Mehta
Aug 6 at 22:34
 |Â
show 3 more comments
1
Why not simply $$(2i,i) mid i in S$$?
– Clement C.
Aug 6 at 22:32
@ClementC. What if $2inotin S$
– Rushabh Mehta
Aug 6 at 22:33
@RushabhMehta Good point. Then it's a bit less nice, indeed: $$(2i,i) mid i in Scap S^2$$
– Clement C.
Aug 6 at 22:34
More, that both are in the set S: $~(2j,j): jin S, 2jin S$
– Graham Kemp
Aug 6 at 22:34
@ClementC. I wouldn't really call that set builder notation
– Rushabh Mehta
Aug 6 at 22:34
1
1
Why not simply $$(2i,i) mid i in S$$?
– Clement C.
Aug 6 at 22:32
Why not simply $$(2i,i) mid i in S$$?
– Clement C.
Aug 6 at 22:32
@ClementC. What if $2inotin S$
– Rushabh Mehta
Aug 6 at 22:33
@ClementC. What if $2inotin S$
– Rushabh Mehta
Aug 6 at 22:33
@RushabhMehta Good point. Then it's a bit less nice, indeed: $$(2i,i) mid i in Scap S^2$$
– Clement C.
Aug 6 at 22:34
@RushabhMehta Good point. Then it's a bit less nice, indeed: $$(2i,i) mid i in Scap S^2$$
– Clement C.
Aug 6 at 22:34
More, that both are in the set S: $~(2j,j): jin S, 2jin S$
– Graham Kemp
Aug 6 at 22:34
More, that both are in the set S: $~(2j,j): jin S, 2jin S$
– Graham Kemp
Aug 6 at 22:34
@ClementC. I wouldn't really call that set builder notation
– Rushabh Mehta
Aug 6 at 22:34
@ClementC. I wouldn't really call that set builder notation
– Rushabh Mehta
Aug 6 at 22:34
 |Â
show 3 more comments
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
That is okay, although the use of words should be discouraged, and it can be compacted a bit more. Â Any of the following should be acceptable: $$(i,j)mid iin S, jin S, i=2j\(2j,j)mid jin S, 2jin S\(i,j) in S^2 mid i= 2 j \(2j,j)in S^2$$
Sometimes there is a trade off between compactness and comprehensibilty. Â Choose the version that you feel most clearly conveys the intended message.
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
add a comment |Â
up vote
0
down vote
It's better if you write: $ i= 2*j $
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
That is okay, although the use of words should be discouraged, and it can be compacted a bit more. Â Any of the following should be acceptable: $$(i,j)mid iin S, jin S, i=2j\(2j,j)mid jin S, 2jin S\(i,j) in S^2 mid i= 2 j \(2j,j)in S^2$$
Sometimes there is a trade off between compactness and comprehensibilty. Â Choose the version that you feel most clearly conveys the intended message.
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
add a comment |Â
up vote
1
down vote
accepted
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
That is okay, although the use of words should be discouraged, and it can be compacted a bit more. Â Any of the following should be acceptable: $$(i,j)mid iin S, jin S, i=2j\(2j,j)mid jin S, 2jin S\(i,j) in S^2 mid i= 2 j \(2j,j)in S^2$$
Sometimes there is a trade off between compactness and comprehensibilty. Â Choose the version that you feel most clearly conveys the intended message.
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
That is okay, although the use of words should be discouraged, and it can be compacted a bit more. Â Any of the following should be acceptable: $$(i,j)mid iin S, jin S, i=2j\(2j,j)mid jin S, 2jin S\(i,j) in S^2 mid i= 2 j \(2j,j)in S^2$$
Sometimes there is a trade off between compactness and comprehensibilty. Â Choose the version that you feel most clearly conveys the intended message.
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
$ (i,j) $ Is it correct and are there any ways to achieve this? Thanks in advance.
That is okay, although the use of words should be discouraged, and it can be compacted a bit more. Â Any of the following should be acceptable: $$(i,j)mid iin S, jin S, i=2j\(2j,j)mid jin S, 2jin S\(i,j) in S^2 mid i= 2 j \(2j,j)in S^2$$
Sometimes there is a trade off between compactness and comprehensibilty. Â Choose the version that you feel most clearly conveys the intended message.
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
edited Aug 6 at 22:46
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
answered Aug 6 at 22:39
Graham Kemp
80.1k43275
80.1k43275
add a comment |Â
add a comment |Â
up vote
0
down vote
It's better if you write: $ i= 2*j $
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
add a comment |Â
up vote
0
down vote
It's better if you write: $ i= 2*j $
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
add a comment |Â
up vote
0
down vote
up vote
0
down vote
It's better if you write: $ i= 2*j $
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
It's better if you write: $ i= 2*j $
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
edited Aug 6 at 23:52
Arnaud Mortier
19.2k22159
19.2k22159
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
answered Aug 6 at 22:42
Juan Fran Gomez Gonzalez
111
111
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
add a comment |Â
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
I don't think including $in S$ in the left part of the set builder notation is considered appropriate, but I am not too knowledgeable on the subject.
– Rushabh Mehta
Aug 6 at 22:45
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
@RushabhMehta It should be $in S^2$, otherwise it is correctly placed. $~(i,j) in S^2 mid i= 2cdot j $ says: the set of pairs, $(i,j)$, drawn from the Cartesian square of $S$ such that $i$ equals twice $j$.
– Graham Kemp
Aug 6 at 22:49
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
It should be $in S^2$. And @RushabhMehta it is appropriate to put $in$ there(some would even say it should be there) as without it it is not guarantee to be a set
– Holo
Aug 6 at 22:51
add a comment |Â
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1
Why not simply $$(2i,i) mid i in S$$?
– Clement C.
Aug 6 at 22:32
@ClementC. What if $2inotin S$
– Rushabh Mehta
Aug 6 at 22:33
@RushabhMehta Good point. Then it's a bit less nice, indeed: $$(2i,i) mid i in Scap S^2$$
– Clement C.
Aug 6 at 22:34
More, that both are in the set S: $~(2j,j): jin S, 2jin S$
– Graham Kemp
Aug 6 at 22:34
@ClementC. I wouldn't really call that set builder notation
– Rushabh Mehta
Aug 6 at 22:34