Does the empty set count as an element? [duplicate]












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  • What is the cardinality of the set of the empty set?

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We're asked the number of elements in a power set and I for {} is the number of elements 1 or 0?






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marked as duplicate by caverac, GNUSupporter 8964民主女神 地下教會, Dietrich Burde, Martin Sleziak, amWhy discrete-mathematics
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 Nov 30 '18 at 22:24


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  • $begingroup$
    Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set.
    $endgroup$
    – saulspatz
    Nov 30 '18 at 19:07
















1












$begingroup$



This question already has an answer here:




  • What is the cardinality of the set of the empty set?

    3 answers




We're asked the number of elements in a power set and I for {} is the number of elements 1 or 0?






discrete-mathematics







share|cite|improve this question









$endgroup$



marked as duplicate by caverac, GNUSupporter 8964民主女神 地下教會, Dietrich Burde, Martin Sleziak, amWhy discrete-mathematics
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 Nov 30 '18 at 22:24


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • $begingroup$
    Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set.
    $endgroup$
    – saulspatz
    Nov 30 '18 at 19:07














1












1








1





$begingroup$



This question already has an answer here:




  • What is the cardinality of the set of the empty set?

    3 answers




We're asked the number of elements in a power set and I for {} is the number of elements 1 or 0?






discrete-mathematics







share|cite|improve this question









$endgroup$





This question already has an answer here:




  • What is the cardinality of the set of the empty set?

    3 answers




We're asked the number of elements in a power set and I for {} is the number of elements 1 or 0?





This question already has an answer here:




  • What is the cardinality of the set of the empty set?

    3 answers







discrete-mathematics




discrete-mathematics






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 30 '18 at 19:04









happysainthappysaint

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marked as duplicate by caverac, GNUSupporter 8964民主女神 地下教會, Dietrich Burde, Martin Sleziak, amWhy discrete-mathematics
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marked as duplicate by caverac, GNUSupporter 8964民主女神 地下教會, Dietrich Burde, Martin Sleziak, amWhy discrete-mathematics
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  • $begingroup$
    Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set.
    $endgroup$
    – saulspatz
    Nov 30 '18 at 19:07


















  • $begingroup$
    Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set.
    $endgroup$
    – saulspatz
    Nov 30 '18 at 19:07
















$begingroup$
Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set.
$endgroup$
– saulspatz
Nov 30 '18 at 19:07




$begingroup$
Yes, it counts. The empty set is a subset of any set, so it will be in the power set of any set.
$endgroup$
– saulspatz
Nov 30 '18 at 19:07










1 Answer
1






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oldest

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$begingroup$

No, an empty set is a subset of every set, not necessarily an element. However, the empty set is an element of the power set of any set.



Notice: $Xsubset Yiff forall x(xin X implies x in Y)$ which is vacously true for any arbitrary set and $emptyset$ since $lnot exists x(xin emptyset)$. However, to say $forall A(emptyset in A)$ implies for a Set $B={a,b,c}$ its $|B|=4$, which is obviously false.



Hope that answers your question.






share|cite|improve this answer











$endgroup$




















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2












    $begingroup$

    No, an empty set is a subset of every set, not necessarily an element. However, the empty set is an element of the power set of any set.



    Notice: $Xsubset Yiff forall x(xin X implies x in Y)$ which is vacously true for any arbitrary set and $emptyset$ since $lnot exists x(xin emptyset)$. However, to say $forall A(emptyset in A)$ implies for a Set $B={a,b,c}$ its $|B|=4$, which is obviously false.



    Hope that answers your question.






    share|cite|improve this answer











    $endgroup$


















      2












      $begingroup$

      No, an empty set is a subset of every set, not necessarily an element. However, the empty set is an element of the power set of any set.



      Notice: $Xsubset Yiff forall x(xin X implies x in Y)$ which is vacously true for any arbitrary set and $emptyset$ since $lnot exists x(xin emptyset)$. However, to say $forall A(emptyset in A)$ implies for a Set $B={a,b,c}$ its $|B|=4$, which is obviously false.



      Hope that answers your question.






      share|cite|improve this answer











      $endgroup$
















        2












        2








        2





        $begingroup$

        No, an empty set is a subset of every set, not necessarily an element. However, the empty set is an element of the power set of any set.



        Notice: $Xsubset Yiff forall x(xin X implies x in Y)$ which is vacously true for any arbitrary set and $emptyset$ since $lnot exists x(xin emptyset)$. However, to say $forall A(emptyset in A)$ implies for a Set $B={a,b,c}$ its $|B|=4$, which is obviously false.



        Hope that answers your question.






        share|cite|improve this answer











        $endgroup$



        No, an empty set is a subset of every set, not necessarily an element. However, the empty set is an element of the power set of any set.



        Notice: $Xsubset Yiff forall x(xin X implies x in Y)$ which is vacously true for any arbitrary set and $emptyset$ since $lnot exists x(xin emptyset)$. However, to say $forall A(emptyset in A)$ implies for a Set $B={a,b,c}$ its $|B|=4$, which is obviously false.



        Hope that answers your question.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Nov 30 '18 at 19:22

























        answered Nov 30 '18 at 19:12









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