- #1
Bachelier
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If you take the intersection of non empty open subsets in Rn as n tends to infinity, such that
[tex]U_1 \supseteq U_2 \supseteq U_3... [/tex]
Is it empty?
[tex]U_1 \supseteq U_2 \supseteq U_3... [/tex]
Is it empty?
Bachelier said:but it can. right?
HallsofIvy said:The fact that this thread was titled "Union of non-empty sets" was a bit confusing!
The union of non empty sets is a mathematical operation that combines all the elements from two or more sets into a single set without any duplicates. It is denoted by the symbol ∪.
The union of non empty sets includes all the elements that are present in at least one of the sets, while the intersection of sets includes only the elements that are common to all the sets.
Yes, the union of non empty sets is commutative and associative. This means that the order in which the sets are combined does not affect the final result, and it can be grouped in any way without changing the outcome.
Yes, the union of non empty sets can be empty if there are no common elements between the sets being combined. In this case, the resulting set will have no elements.
The union of non empty sets is used in various fields such as statistics, computer science, and economics. It is used to represent the combination of different data sets, the merging of multiple databases, and the calculation of probabilities in decision making.