Why is every set a subset of itself

Please tell me. Do all sets, even the empty set, have infitinite emptiness e. There is only one empty set. It is a subset of every set, including itself. Each set only includes it once as a subset, not an infinite number of times. The empty set is subset of the empty set, as every element of the empty set is an element of the empty set.

This happens for example in category theory, as you are only interested in abstract sets, and all sets of the same cardinality are in a sense the same, you just title finite sets by their cardinality.

Any set is a subset of itself. The intersection of two sets is a subset of each of the original sets. By the definition of subset this question means: Is every element of the empty set a member of the empty set?

The answer must be yes, since the empty set doesn't contain any elements. An empty subset can be selected from any set, including the empty set itself, using selection criteria that cannot be satisfied, e. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

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