If an empty set is a subset of any set, is it a proper subset of any set?

If an empty set is a subset of any set, is it a proper subset of any set?


Except for the empty set itself, yes



An empty set is a proper subset of any set______ .


According to the meaning of the question, if an empty set is a subset of any set and a proper subset of any nonempty set, that is to say, an empty set is not a proper subset of itself, then the original proposition is wrong, so the answer is ×



Why do we say "an element empty set is a proper subset of a set (which contains only one element of an empty set)"
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Φ is the proper subset of {Φ}


Because an empty set is a proper subset of any nonempty set
But {Φ} is not an empty set, but a set whose elements are empty sets. This set has elements, and this element is an empty set. It is a special case that an empty set is an element



An empty set is a proper subset of any nonempty set


(1) An empty set is a subset of any set
(2) If an empty set is a non proper subset of a set, only a is an empty set