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Q: Why empty set is proper subset of every set?

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Because every set is a subset of itself. A proper subset cannot, however, be a proper subset of itself.

The empty set has only one subset: itself. It has no proper subsets.

Since B is a subset of A, all elements of B are in A.If the elements of B are deleted, then B is an empty set, and also it is a subset of A, moreover B is a proper subset of A.

The collection of all sets minus the empty set is not a set (it is too big to be a set) but instead a proper class. See Russell's paradox for why it would be problematic to consider this a set. According to axioms of standard ZFC set theory, not every intuitive "collection" of sets is a set; we must proceed carefully when reasoning about what is a set according to ZFC.

An improper subset is identical to the set of which it is a subset. For example: Set A: {1, 2, 3, 4, 5} Set B: {1, 2, 3, 4, 5} Set B is an improper subset of Set Aand vice versa.

Related questions

An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.

yes, if the set being described is empty, we can talk about proper and improper subsets. there are no proper subsets of the empty set. the only subset of the empty set is the empty set itself. to be a proper subset, the subset must be strictly contained. so the empty set is an improper subset of itself, but it is a proper subset of every other set.

Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.

Yes.

The empty set.

Every set contains the empty set. Every set is a subset of itself.

NO

Yes

The empty set!

No. The empty is the a subset of every set and every set is a subset of itself.

No. An empty set is a subset of every set but it is not an element of every set.

Yes, it is

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