Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is $\{\}, \, \{\{\}\},\, \{\{\{\}\}\}$ is an empty set or not?

My opinion: the first is the empty set because it contains no elements, while the second and third are not an empty set because it contains a empty set.

Please explain to me the given question in detail.

share|improve this question
    
Can you define each of them? Remember that $\{ \varnothing \} \ne \varnothing$. Also, $\varnothing \notin \{ \{ \varnothing \} \}$ (you mentioned that the third set contains the empty set) –  Andrew Salmon Apr 22 '13 at 5:46
    
If by double brackets you mean $\{ \} = \emptyset$, then you're correct. The second two are not empty and the first one is. –  Suugaku Apr 22 '13 at 5:47
    
Thanks friends got it –  juantheron Apr 22 '13 at 5:49

1 Answer 1

Yes. The first set is the only empty set. To convince yourself that the other two are not empty sets, try to answer these two questions:

$1$. Is a bag containing an empty bag empty?

$2$. Is a bag containing a bag, that contains an empty bag, empty?

share|improve this answer
    
Thanks user17762 got it –  juantheron Apr 22 '13 at 5:50

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.