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Can I make a set containing the empty set using the ZFC axioms [closed]

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-1

$begingroup$

$A = 1$. Can the set $2, 3, varnothing$ be constructed from $A$ using ZFC? If not, explain why. If so, show the construction through the axioms.

elementary-set-theory

share|cite|improve this question

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

asked Mar 14 at 17:32

user652437user652437

11

$endgroup$

closed as off-topic by Greg Martin, Noah Schweber, Vinyl_cape_jawa, José Carlos Santos, Cesareo Mar 15 at 0:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Greg Martin, Noah Schweber, Vinyl_cape_jawa, José Carlos Santos, Cesareo

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
  $endgroup$
  – Greg Martin
  Mar 14 at 17:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you do any of it? Can you make $2?$
  $endgroup$
  – Ross Millikan
  Mar 14 at 17:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I can do it up until the part with the empty set so I'm contemplating between 2 answers and I want to know which part is correct. Either; I can make the set and use replacement to create ∅ from set A at which point I know how to use the axioms to make the rest of the set. Or its impossible to use replacement to get the empty set at which point I don't believe I can construct the set
  $endgroup$
  – user652437
  Mar 14 at 18:02
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is the definition of $1$, $2$ and $3$? Where does this question come from?
  $endgroup$
  – Somos
  Mar 14 at 19:12
  
  

  
  
  
  

add a comment | 

-1

$begingroup$

$A = 1$. Can the set $2, 3, varnothing$ be constructed from $A$ using ZFC? If not, explain why. If so, show the construction through the axioms.

elementary-set-theory

share|cite|improve this question

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

asked Mar 14 at 17:32

user652437user652437

11

$endgroup$

closed as off-topic by Greg Martin, Noah Schweber, Vinyl_cape_jawa, José Carlos Santos, Cesareo Mar 15 at 0:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Greg Martin, Noah Schweber, Vinyl_cape_jawa, José Carlos Santos, Cesareo

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts? What have you tried? Where are you stuck? You need to provide context for your question. Right now, it just looks like you want somebody to do your homework for you; that's not what this site is for. If you add some appropriate context, we will be happy to help.
  $endgroup$
  – Greg Martin
  Mar 14 at 17:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Can you do any of it? Can you make $2?$
  $endgroup$
  – Ross Millikan
  Mar 14 at 17:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I can do it up until the part with the empty set so I'm contemplating between 2 answers and I want to know which part is correct. Either; I can make the set and use replacement to create ∅ from set A at which point I know how to use the axioms to make the rest of the set. Or its impossible to use replacement to get the empty set at which point I don't believe I can construct the set
  $endgroup$
  – user652437
  Mar 14 at 18:02
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is the definition of $1$, $2$ and $3$? Where does this question come from?
  $endgroup$
  – Somos
  Mar 14 at 19:12
  
  

  
  
  
  

add a comment | 

$begingroup$

$A = 1$. Can the set $2, 3, varnothing$ be constructed from $A$ using ZFC? If not, explain why. If so, show the construction through the axioms.

elementary-set-theory

share|cite|improve this question

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

asked Mar 14 at 17:32

user652437user652437

11

$endgroup$

share|cite|improve this question

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

asked Mar 14 at 17:32

user652437user652437

11

share|cite|improve this question

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

asked Mar 14 at 17:32

user652437user652437

11

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

edited Mar 14 at 17:58

Asaf Karagila♦

306k33438769

asked Mar 14 at 17:32

user652437user652437

11

asked Mar 14 at 17:32

user652437user652437

11