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The whole universe

In

set theory, the '

universal set, denoted U

, is the set containing all the existing collections. Each existing set is a subset of the universe, then we can say that U

also contains all the existing elements. Each set is included in U and U includes all sets

.

Property whole universe

The universal set is unique Includes all other existing sets Each element belongs to U
The union of a set with the ' universal set is the whole universe itself

The intersection of a set A with the whole universe is the same set A The only collection that contains the universal set is the whole universe itself

It is said that the whole universe is unique because it is not properly identified as "a universal set", as it is one and then it says "the whole universe" .
• course also contains a whole universe itself and the empty set. That is
and {U}.
Source:
• Wikipedia - the universal set in algebra