How do I define a set of statements of the form x∈A in set builder notation?
1
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I would like to define a set with set builder notation where all elements are of the form "x ∈ A." For example, with a set B = {x ∈ A, y ∈ A, ... , z ∈ A} it would be tempting to define B as B = {a ∈ A | a ∈ A} but in this case "a ∈ A" is just taken to mean "a" which is an element of "A" so it would be that B = {x , y, ..., z} which is not what I want. How would one define a set of statements, such as B, in set builder notation without making it misleading?
elementary-set-theory notation
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
$endgroup$
|
show 5 more comments
1
$begingroup$
I would like to define a set with set builder notation where all elements are of the form "x ∈ A." For example, with a set B = {x ∈ A, y ∈ A, ... , z ∈ A} it would be tempting to define B as B = {a ∈ A | a ∈ A} but in this case "a ∈ A" is just taken to mean "a" which is an element of "A" so it would be that B = {x , y, ..., z} which is not what I want. How would one define a set of statements, such as B, in set builder notation without making it misleading?
elementary-set-theory notation
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
$endgroup$
1
$begingroup$
What does "of the form $xin A$" mean? Either $x$ is also in $A$ or $x$ is not in $A$.
$endgroup$
– Joey Kilpatrick
Dec 1 '18 at 7:27
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
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– José Carlos Santos
Dec 1 '18 at 7:28
1
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I don't understand, why not just write $A$? $A$ is the set of all elements $x in A$.
$endgroup$
– AlephZero
Dec 1 '18 at 7:43
$begingroup$
Your question is confusing. What exactly are you trying to ask? As @AlephZero rightly said, $A$ is the set of every $ain A$. Why not just write A?.
$endgroup$
– Bertrand Wittgenstein's Ghost
Dec 1 '18 at 7:46
$begingroup$
I don't want B to be the set of all elements in A; I want B to be the set of all "statements," such as "x is an element of A," "y is an element of A," and so forth.
$endgroup$
– Cam White
Dec 1 '18 at 7:48
|
show 5 more comments
1
1
1
$begingroup$
I would like to define a set with set builder notation where all elements are of the form "x ∈ A." For example, with a set B = {x ∈ A, y ∈ A, ... , z ∈ A} it would be tempting to define B as B = {a ∈ A | a ∈ A} but in this case "a ∈ A" is just taken to mean "a" which is an element of "A" so it would be that B = {x , y, ..., z} which is not what I want. How would one define a set of statements, such as B, in set builder notation without making it misleading?
elementary-set-theory notation
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
$endgroup$
I would like to define a set with set builder notation where all elements are of the form "x ∈ A." For example, with a set B = {x ∈ A, y ∈ A, ... , z ∈ A} it would be tempting to define B as B = {a ∈ A | a ∈ A} but in this case "a ∈ A" is just taken to mean "a" which is an element of "A" so it would be that B = {x , y, ..., z} which is not what I want. How would one define a set of statements, such as B, in set builder notation without making it misleading?
elementary-set-theory notation
elementary-set-theory notation
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
edited Dec 1 '18 at 14:11
Andrés E. Caicedo
65k8158246
65k8158246
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
asked Dec 1 '18 at 7:24
Cam WhiteCam White
61
61
1
$begingroup$
What does "of the form $xin A$" mean? Either $x$ is also in $A$ or $x$ is not in $A$.
$endgroup$
– Joey Kilpatrick
Dec 1 '18 at 7:27
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Dec 1 '18 at 7:28
1
$begingroup$
I don't understand, why not just write $A$? $A$ is the set of all elements $x in A$.
$endgroup$
– AlephZero
Dec 1 '18 at 7:43
$begingroup$
Your question is confusing. What exactly are you trying to ask? As @AlephZero rightly said, $A$ is the set of every $ain A$. Why not just write A?.
$endgroup$
– Bertrand Wittgenstein's Ghost
Dec 1 '18 at 7:46
$begingroup$
I don't want B to be the set of all elements in A; I want B to be the set of all "statements," such as "x is an element of A," "y is an element of A," and so forth.
$endgroup$
– Cam White
Dec 1 '18 at 7:48
|
show 5 more comments
1
$begingroup$
What does "of the form $xin A$" mean? Either $x$ is also in $A$ or $x$ is not in $A$.
$endgroup$
– Joey Kilpatrick
Dec 1 '18 at 7:27
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Dec 1 '18 at 7:28
1
$begingroup$
I don't understand, why not just write $A$? $A$ is the set of all elements $x in A$.
$endgroup$
– AlephZero
Dec 1 '18 at 7:43
$begingroup$
Your question is confusing. What exactly are you trying to ask? As @AlephZero rightly said, $A$ is the set of every $ain A$. Why not just write A?.
$endgroup$
– Bertrand Wittgenstein's Ghost
Dec 1 '18 at 7:46
$begingroup$
I don't want B to be the set of all elements in A; I want B to be the set of all "statements," such as "x is an element of A," "y is an element of A," and so forth.
$endgroup$
– Cam White
Dec 1 '18 at 7:48
1
1
$begingroup$
What does "of the form $xin A$" mean? Either $x$ is also in $A$ or $x$ is not in $A$.
$endgroup$
– Joey Kilpatrick
Dec 1 '18 at 7:27
$begingroup$
What does "of the form $xin A$" mean? Either $x$ is also in $A$ or $x$ is not in $A$.
$endgroup$
– Joey Kilpatrick
Dec 1 '18 at 7:27
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Dec 1 '18 at 7:28
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Dec 1 '18 at 7:28
1
1
$begingroup$
I don't understand, why not just write $A$? $A$ is the set of all elements $x in A$.
$endgroup$
– AlephZero
Dec 1 '18 at 7:43
$begingroup$
I don't understand, why not just write $A$? $A$ is the set of all elements $x in A$.
$endgroup$
– AlephZero
Dec 1 '18 at 7:43
$begingroup$
Your question is confusing. What exactly are you trying to ask? As @AlephZero rightly said, $A$ is the set of every $ain A$. Why not just write A?.
$endgroup$
– Bertrand Wittgenstein's Ghost
Dec 1 '18 at 7:46
$begingroup$
Your question is confusing. What exactly are you trying to ask? As @AlephZero rightly said, $A$ is the set of every $ain A$. Why not just write A?.
$endgroup$
– Bertrand Wittgenstein's Ghost
Dec 1 '18 at 7:46
$begingroup$
I don't want B to be the set of all elements in A; I want B to be the set of all "statements," such as "x is an element of A," "y is an element of A," and so forth.
$endgroup$
– Cam White
Dec 1 '18 at 7:48
$begingroup$
I don't want B to be the set of all elements in A; I want B to be the set of all "statements," such as "x is an element of A," "y is an element of A," and so forth.
$endgroup$
– Cam White
Dec 1 '18 at 7:48
|
show 5 more comments
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1
$begingroup$
What does "of the form $xin A$" mean? Either $x$ is also in $A$ or $x$ is not in $A$.
$endgroup$
– Joey Kilpatrick
Dec 1 '18 at 7:27
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Dec 1 '18 at 7:28
1
$begingroup$
I don't understand, why not just write $A$? $A$ is the set of all elements $x in A$.
$endgroup$
– AlephZero
Dec 1 '18 at 7:43
$begingroup$
Your question is confusing. What exactly are you trying to ask? As @AlephZero rightly said, $A$ is the set of every $ain A$. Why not just write A?.
$endgroup$
– Bertrand Wittgenstein's Ghost
Dec 1 '18 at 7:46
$begingroup$
I don't want B to be the set of all elements in A; I want B to be the set of all "statements," such as "x is an element of A," "y is an element of A," and so forth.
$endgroup$
– Cam White
Dec 1 '18 at 7:48