Set theory - axiom of powers

Clash Royale CLAN TAG#URR8PPP

up vote
0
down vote

favorite

I am reading Halmos' Naive Set Theory.

He writes: If $mathcal C $ is a collection of subsets of a set $ E $ (that is, $mathcal C $ is a subcollection of power set $ wp(E) $), then write

$mathcal D = X in wp(E):X^complementin mathcal C $

If $E = 1,2 $ and $mathcal C = 1,2 $ does $mathcal C =mathcal D $?

Thanks in advance,

elementary-set-theory

share|cite|improve this question

edited Jul 30 at 9:11

drhab

85.9k540118

asked Jul 30 at 8:51

Paul

104

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Is $X'=Esetminus X$?
  – Saucy O'Path
  Jul 30 at 8:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm not sure it does not mention what X is.
  – Paul
  Jul 30 at 8:58
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the book mention what the $'$ symbol means?
  – bof
  Jul 30 at 9:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes... an often used symbol for the temporarily absolute (as opposed to relative) complement of A is A'.
  – Paul
  Jul 30 at 9:08
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I am reading Halmos' Naive Set Theory.

He writes: If $mathcal C $ is a collection of subsets of a set $ E $ (that is, $mathcal C $ is a subcollection of power set $ wp(E) $), then write

$mathcal D = X in wp(E):X^complementin mathcal C $

If $E = 1,2 $ and $mathcal C = 1,2 $ does $mathcal C =mathcal D $?

Thanks in advance,

elementary-set-theory

share|cite|improve this question

edited Jul 30 at 9:11

drhab

85.9k540118

asked Jul 30 at 8:51

Paul

104

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Is $X'=Esetminus X$?
  – Saucy O'Path
  Jul 30 at 8:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm not sure it does not mention what X is.
  – Paul
  Jul 30 at 8:58
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the book mention what the $'$ symbol means?
  – bof
  Jul 30 at 9:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes... an often used symbol for the temporarily absolute (as opposed to relative) complement of A is A'.
  – Paul
  Jul 30 at 9:08
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I am reading Halmos' Naive Set Theory.

He writes: If $mathcal C $ is a collection of subsets of a set $ E $ (that is, $mathcal C $ is a subcollection of power set $ wp(E) $), then write

$mathcal D = X in wp(E):X^complementin mathcal C $

If $E = 1,2 $ and $mathcal C = 1,2 $ does $mathcal C =mathcal D $?

Thanks in advance,

elementary-set-theory

share|cite|improve this question

edited Jul 30 at 9:11

drhab

85.9k540118

asked Jul 30 at 8:51

Paul

104

I am reading Halmos' Naive Set Theory.

He writes: If $mathcal C $ is a collection of subsets of a set $ E $ (that is, $mathcal C $ is a subcollection of power set $ wp(E) $), then write

$mathcal D = X in wp(E):X^complementin mathcal C $

If $E = 1,2 $ and $mathcal C = 1,2 $ does $mathcal C =mathcal D $?

Thanks in advance,

elementary-set-theory

share|cite|improve this question

edited Jul 30 at 9:11

drhab

85.9k540118

asked Jul 30 at 8:51

Paul

104

share|cite|improve this question

share|cite|improve this question

edited Jul 30 at 9:11

drhab

85.9k540118

edited Jul 30 at 9:11

drhab

85.9k540118

edited Jul 30 at 9:11

drhab

85.9k540118

85.9k540118

asked Jul 30 at 8:51

Paul

104

asked Jul 30 at 8:51

Paul

104

asked Jul 30 at 8:51

Paul

104

104

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Is $X'=Esetminus X$?
  – Saucy O'Path
  Jul 30 at 8:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm not sure it does not mention what X is.
  – Paul
  Jul 30 at 8:58
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the book mention what the $'$ symbol means?
  – bof
  Jul 30 at 9:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes... an often used symbol for the temporarily absolute (as opposed to relative) complement of A is A'.
  – Paul
  Jul 30 at 9:08
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Is $X'=Esetminus X$?
  – Saucy O'Path
  Jul 30 at 8:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I'm not sure it does not mention what X is.
  – Paul
  Jul 30 at 8:58
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Does the book mention what the $'$ symbol means?
  – bof
  Jul 30 at 9:06
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Yes... an often used symbol for the temporarily absolute (as opposed to relative) complement of A is A'.
  – Paul
  Jul 30 at 9:08
  

  
  
  
  

Is $X'=Esetminus X$?
– Saucy O'Path
Jul 30 at 8:57

Is $X'=Esetminus X$?
– Saucy O'Path
Jul 30 at 8:57

I'm not sure it does not mention what X is.
– Paul
Jul 30 at 8:58

I'm not sure it does not mention what X is.
– Paul
Jul 30 at 8:58

Does the book mention what the $'$ symbol means?
– bof
Jul 30 at 9:06

Does the book mention what the $'$ symbol means?
– bof
Jul 30 at 9:06

Yes... an often used symbol for the temporarily absolute (as opposed to relative) complement of A is A'.
– Paul
Jul 30 at 9:08

Yes... an often used symbol for the temporarily absolute (as opposed to relative) complement of A is A'.
– Paul
Jul 30 at 9:08

add a comment | 

1 Answer
1

active

oldest

votes

up vote
0
down vote



accepted

The answer is "yes".

$mathcal D=Xinwp(E)mid X^complementin1,2=1^complement,2^complement=2,1=mathcal C$

share|cite|improve this answer

answered Jul 30 at 9:08

drhab

85.9k540118

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you! I've asked this question on here before but I've never had an answer
  – Paul
  Jul 30 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You are welcome. Check the edit of the question and get familiar with MathJax.
  – drhab
  Jul 30 at 9:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  s see, does the small c denote a compelment of C?
  – Paul
  Jul 30 at 9:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $A^complement$ denotes the complement of $A$. In your case the set $E-A$.
  – drhab
  Jul 30 at 9:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  There is no A in my example?
  – Paul
  Jul 30 at 9:47
  

  
  
  
  

 | 
show 2 more comments

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2866790%2fset-theory-axiom-of-powers%23new-answer', 'question_page');

);

Post as a guest

Name Email

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote



accepted

The answer is "yes".

$mathcal D=Xinwp(E)mid X^complementin1,2=1^complement,2^complement=2,1=mathcal C$

share|cite|improve this answer

answered Jul 30 at 9:08

drhab

85.9k540118

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you! I've asked this question on here before but I've never had an answer
  – Paul
  Jul 30 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You are welcome. Check the edit of the question and get familiar with MathJax.
  – drhab
  Jul 30 at 9:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  s see, does the small c denote a compelment of C?
  – Paul
  Jul 30 at 9:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $A^complement$ denotes the complement of $A$. In your case the set $E-A$.
  – drhab
  Jul 30 at 9:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  There is no A in my example?
  – Paul
  Jul 30 at 9:47
  

  
  
  
  

 | 
show 2 more comments

up vote
0
down vote



accepted

The answer is "yes".

$mathcal D=Xinwp(E)mid X^complementin1,2=1^complement,2^complement=2,1=mathcal C$

share|cite|improve this answer

answered Jul 30 at 9:08

drhab

85.9k540118

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you! I've asked this question on here before but I've never had an answer
  – Paul
  Jul 30 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You are welcome. Check the edit of the question and get familiar with MathJax.
  – drhab
  Jul 30 at 9:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  s see, does the small c denote a compelment of C?
  – Paul
  Jul 30 at 9:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $A^complement$ denotes the complement of $A$. In your case the set $E-A$.
  – drhab
  Jul 30 at 9:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  There is no A in my example?
  – Paul
  Jul 30 at 9:47
  

  
  
  
  

 | 
show 2 more comments

up vote
0
down vote



accepted

up vote
0
down vote



accepted

The answer is "yes".

$mathcal D=Xinwp(E)mid X^complementin1,2=1^complement,2^complement=2,1=mathcal C$

share|cite|improve this answer

answered Jul 30 at 9:08

drhab

85.9k540118

The answer is "yes".

$mathcal D=Xinwp(E)mid X^complementin1,2=1^complement,2^complement=2,1=mathcal C$

share|cite|improve this answer

answered Jul 30 at 9:08

drhab

85.9k540118

share|cite|improve this answer

share|cite|improve this answer

answered Jul 30 at 9:08

drhab

85.9k540118

answered Jul 30 at 9:08

drhab

85.9k540118

answered Jul 30 at 9:08

drhab

85.9k540118

85.9k540118

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you! I've asked this question on here before but I've never had an answer
  – Paul
  Jul 30 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You are welcome. Check the edit of the question and get familiar with MathJax.
  – drhab
  Jul 30 at 9:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  s see, does the small c denote a compelment of C?
  – Paul
  Jul 30 at 9:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $A^complement$ denotes the complement of $A$. In your case the set $E-A$.
  – drhab
  Jul 30 at 9:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  There is no A in my example?
  – Paul
  Jul 30 at 9:47
  

  
  
  
  

 | 
show 2 more comments

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you! I've asked this question on here before but I've never had an answer
  – Paul
  Jul 30 at 9:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  You are welcome. Check the edit of the question and get familiar with MathJax.
  – drhab
  Jul 30 at 9:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  s see, does the small c denote a compelment of C?
  – Paul
  Jul 30 at 9:20
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $A^complement$ denotes the complement of $A$. In your case the set $E-A$.
  – drhab
  Jul 30 at 9:21
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  There is no A in my example?
  – Paul
  Jul 30 at 9:47
  

  
  
  
  

Thank you! I've asked this question on here before but I've never had an answer
– Paul
Jul 30 at 9:10

Thank you! I've asked this question on here before but I've never had an answer
– Paul
Jul 30 at 9:10

You are welcome. Check the edit of the question and get familiar with MathJax.
– drhab
Jul 30 at 9:13

You are welcome. Check the edit of the question and get familiar with MathJax.
– drhab
Jul 30 at 9:13

s see, does the small c denote a compelment of C?
– Paul
Jul 30 at 9:20

s see, does the small c denote a compelment of C?
– Paul
Jul 30 at 9:20

$A^complement$ denotes the complement of $A$. In your case the set $E-A$.
– drhab
Jul 30 at 9:21

$A^complement$ denotes the complement of $A$. In your case the set $E-A$.
– drhab
Jul 30 at 9:21

There is no A in my example?
– Paul
Jul 30 at 9:47

There is no A in my example?
– Paul
Jul 30 at 9:47

 | 
show 2 more comments

 

draft saved

draft discarded

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2866790%2fset-theory-axiom-of-powers%23new-answer', 'question_page');

);

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Name Email

Name

Email

Name Email

Name

Email