Math 2.0

definition

Union of a family of sets

Definition

Let (Ai)i∈I(A_i)_{i \in I} be a family of sets. The union of the family is the set ⋃i∈IAi={x∣∃i∈I, x∈Ai}.\bigcup_{i \in I} A_i = \{x \mid \exists i \in I, \, x \in A_i\}. So xx is an element of the union when x∈Aix \in A_i for at least one i∈Ii \in I.

Remarks

For I={1,2}I = \{1, 2\}, this is the union A1∪A2A_1 \cup A_2. For an empty index set, the union is the empty set. Example: ⋃n≥1[0,n]=[0,∞)\bigcup_{n \ge 1} [0, n] = [0, \infty) in R\mathbb{R}.

Explanations

L1 human

The union of a family collects every element that appears in some member of the family. It generalizes A∪BA \cup B from two sets to any number of sets.

What this node needs for W2
  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

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Sources

  1. Web https://en.wikipedia.org/wiki/Union_(set_theory), Arbitrary union

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