Is ∅ equivalent to {∅}? [duplicate]
Is ∅ equivalent to {∅}? I think they are, but I am not sure? If anyone could clarify, that would be great. Thank you!
No. $\emptyset$ has zero elements, and $\{\emptyset\}$ has one element.
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.
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.
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.