Is ∅ equivalent to {∅}? I think they are, but I am not sure? If anyone could clarify, that would be great. Thank you!
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4"Equivalent" meaning here...? – Timbuc Sep 22 '14 at 03:39
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1I'm going to have to say no.. for one thing the cardinalities of the two sets are not equal. – graydad Sep 22 '14 at 03:40
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See here, here and here – Joel Bosveld Sep 22 '14 at 03:46
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No... one is just an empty set while the second one has just one element which is the empty set. So, first one... empty set ONLY and second one... there's a set with one element and it's an empty set. – usukidoll Sep 22 '14 at 03:53
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5I think this question has been asked at least a thousand times before. – Asaf Karagila Sep 22 '14 at 03:53
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No, absolutely no.... $\emptyset$ has no elements and ${\emptyset}$ has one.. – Jearson Narvaez Rojas Sep 22 '14 at 04:01
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1Absolutely not! The set ${\emptyset}$ contains $\emptyset$, whereas $\emptyset$ contains nothing. Edit: @JearsonNarvaezRojas beat me to the punch. – Robin Goodfellow Sep 22 '14 at 04:01
4 Answers
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It seems that you are confused about notation. Two common ways to denote the empty set are $\emptyset$ and $\{\}$. Using alternate notation the question becomes is $\{\}$ equivalent to $\{\emptyset\}$. Note that $\{\emptyset\}$ is a set of sets. It is a set containing a single element, and that element is the empty set. On the other hand, the empty set is a set containing zero elements.
Eric
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The set of an empty set is not an empty set. $\qquad\{\{\}\}\not\equiv\{\}$
It has an element, even if that element is itself a set with no elements.
Graham Kemp
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No! they are not the same. Simple answer: The cardinality of a set containing an empty set is 1, whilst the empty set itself is 0.
Aaron
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