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The set union is defined for only two sets. Sometimes, it is convenient to have a more general definition involving an arbitrary number of sets.

Definition: Generalized Union of Sets

Let $X_i\text{ , }i\in I$ be a family of sets over the index set $I$. A union of sets of $X_i\text{ , }i\in I$ is denoted and defined by $$\bigcup_{i\in I}X_i:=\{x\in X\mid \exists i\in I\text{, }x\in X_i\}.$$

Notes

1 The concept of countable/uncountable will be introduced, when we will be studying cardinal numbers.

| | | | | created: 2019-09-08 10:17:36 | modified: 2019-09-08 10:25:02 | by: bookofproofs | references: [8297]

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Bibliography (further reading)

[8297] Flachsmeyer, J├╝rgen: “Kombinatorik”, VEB Deutscher Verlag der Wissenschaften, 1972, Dritte Auflage