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Is equipotent $sim$ relation?

0

$begingroup$

Problem: $sim$ is the mark for bijection between two set. Let $A$, $B$, $C$ be sets. Then$$A sim A\Asim B Rightarrow Bsim A\(Asim B land Bsim C )Rightarrow Asim C$$
I know that is not a relation because it is define on set that contains all set which is not set. But my professor told that if I write like this it is OK.

Let $A,B,Csubset U$ where $U$ is some universal set. Then$$A sim A\Asim B Rightarrow Bsim A\(Asim B land Bsim C )Rightarrow Asim C$$
Because I define relation $sim$ on $P(U) × P(U)$ Is this correct?

elementary-set-theory relations

share|cite|improve this question

edited Mar 19 at 11:43

Saad

20.3k92352

asked Mar 19 at 11:34

josfjosf

286317

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's correct.
  $endgroup$
  – Floris Claassens
  Mar 19 at 11:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is a relation on $wp(U)$ or equivalently a subset of $wp(U)timeswp(U)$.
  $endgroup$
  – drhab
  Mar 19 at 11:41
  

  
  
  
  

add a comment | 

0

$begingroup$

Problem: $sim$ is the mark for bijection between two set. Let $A$, $B$, $C$ be sets. Then$$A sim A\Asim B Rightarrow Bsim A\(Asim B land Bsim C )Rightarrow Asim C$$
I know that is not a relation because it is define on set that contains all set which is not set. But my professor told that if I write like this it is OK.

Let $A,B,Csubset U$ where $U$ is some universal set. Then$$A sim A\Asim B Rightarrow Bsim A\(Asim B land Bsim C )Rightarrow Asim C$$
Because I define relation $sim$ on $P(U) × P(U)$ Is this correct?

elementary-set-theory relations

share|cite|improve this question

edited Mar 19 at 11:43

Saad

20.3k92352

asked Mar 19 at 11:34

josfjosf

286317

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, that's correct.
  $endgroup$
  – Floris Claassens
  Mar 19 at 11:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It is a relation on $wp(U)$ or equivalently a subset of $wp(U)timeswp(U)$.
  $endgroup$
  – drhab
  Mar 19 at 11:41
  

  
  
  
  

add a comment | 

$begingroup$

Problem: $sim$ is the mark for bijection between two set. Let $A$, $B$, $C$ be sets. Then$$A sim A\Asim B Rightarrow Bsim A\(Asim B land Bsim C )Rightarrow Asim C$$
I know that is not a relation because it is define on set that contains all set which is not set. But my professor told that if I write like this it is OK.

Let $A,B,Csubset U$ where $U$ is some universal set. Then$$A sim A\Asim B Rightarrow Bsim A\(Asim B land Bsim C )Rightarrow Asim C$$
Because I define relation $sim$ on $P(U) × P(U)$ Is this correct?

elementary-set-theory relations

share|cite|improve this question

edited Mar 19 at 11:43

Saad

20.3k92352

asked Mar 19 at 11:34

josfjosf

286317

$endgroup$

share|cite|improve this question

edited Mar 19 at 11:43

Saad

20.3k92352

asked Mar 19 at 11:34

josfjosf

286317

share|cite|improve this question

edited Mar 19 at 11:43

Saad

20.3k92352

asked Mar 19 at 11:34

josfjosf

286317

edited Mar 19 at 11:43

Saad

20.3k92352

edited Mar 19 at 11:43

Saad

20.3k92352

asked Mar 19 at 11:34

josfjosf

286317

asked Mar 19 at 11:34

josfjosf

286317