“a” is an element of a set of a set of “a”?

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5
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I'm having a hard time conceptualizing what this means:

$a in a$

Is this saying that the a is an element of the set of set a?

elementary-set-theory

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edited yesterday

asked yesterday

edmonda7

413

add a comment | 

up vote
5
down vote

favorite

I'm having a hard time conceptualizing what this means:

$a in a$

Is this saying that the a is an element of the set of set a?

elementary-set-theory

share|cite|improve this question

edited yesterday

asked yesterday

edmonda7

413

add a comment | 

up vote
5
down vote

favorite

up vote
5
down vote

favorite

I'm having a hard time conceptualizing what this means:

$a in a$

Is this saying that the a is an element of the set of set a?

elementary-set-theory

share|cite|improve this question

edited yesterday

asked yesterday

edmonda7

413

I'm having a hard time conceptualizing what this means:

$a in a$

Is this saying that the a is an element of the set of set a?

elementary-set-theory

elementary-set-theory

share|cite|improve this question

edited yesterday

asked yesterday

edmonda7

413

share|cite|improve this question

edited yesterday

asked yesterday

edmonda7

413

share|cite|improve this question

share|cite|improve this question

edited yesterday

edited yesterday

edited yesterday

asked yesterday

edmonda7

413

asked yesterday

edmonda7

413

asked yesterday

edmonda7

413

413

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

up vote
7
down vote

Yep, that's what the statement says. The statement is false, but you have interpreted it correctly.

share|cite|improve this answer

answered yesterday

Theo Bendit

12.9k1944

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
  – edmonda7
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
  – Theo Bendit
  yesterday
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
  – Arthur
  yesterday
  
  

  
  
  
  

 | 
show 3 more comments

Your Answer

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
7
down vote

Yep, that's what the statement says. The statement is false, but you have interpreted it correctly.

share|cite|improve this answer

answered yesterday

Theo Bendit

12.9k1944

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
  – edmonda7
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
  – Theo Bendit
  yesterday
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
  – Arthur
  yesterday
  
  

  
  
  
  

 | 
show 3 more comments

up vote
7
down vote

Yep, that's what the statement says. The statement is false, but you have interpreted it correctly.

share|cite|improve this answer

answered yesterday

Theo Bendit

12.9k1944

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
  – edmonda7
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
  – Theo Bendit
  yesterday
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
  – Arthur
  yesterday
  
  

  
  
  
  

 | 
show 3 more comments

up vote
7
down vote

up vote
7
down vote

Yep, that's what the statement says. The statement is false, but you have interpreted it correctly.

share|cite|improve this answer

answered yesterday

Theo Bendit

12.9k1944

Yep, that's what the statement says. The statement is false, but you have interpreted it correctly.

share|cite|improve this answer

answered yesterday

Theo Bendit

12.9k1944

share|cite|improve this answer

share|cite|improve this answer

answered yesterday

Theo Bendit

12.9k1944

answered yesterday

Theo Bendit

12.9k1944

answered yesterday

Theo Bendit

12.9k1944

12.9k1944

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
  – edmonda7
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
  – Theo Bendit
  yesterday
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
  – Arthur
  yesterday
  
  

  
  
  
  

 | 
show 3 more comments

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
  – edmonda7
  yesterday
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
  – xbh
  yesterday
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
  – Theo Bendit
  yesterday
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
  – Arthur
  yesterday
  
  

  
  
  
  

1

1

A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
– xbh
yesterday

A little flaw here: should it be "the element $a$ is an element of the set of set of $a$"?
– xbh
yesterday

So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
– edmonda7
yesterday

So, if i'm understanding correctly, it is false because a is defined as an element and an element cannot belong to a set that contains another set of itself?
– edmonda7
yesterday

Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
– xbh
yesterday

Now that I think about it, the correct statement should be the title you gave, however it does not match your post entirely.
– xbh
yesterday

2

2

Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
– Theo Bendit
yesterday

Indeed, $a = lbrace a rbrace$ violates the axiom of regularity.
– Theo Bendit
yesterday

1

1

@xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
– Arthur
yesterday

@xbh Yes, it can. Not in ZF set theory, but logically there is nothing wrong with $a=a$.
– Arthur
yesterday

 | 
show 3 more comments

 

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