Cartesian product and set families - definitions and theorems

Unordered pair

An unordered pair is a two-element set {a, b}

Ordered pair

An ordered pair ⟨a, b⟩ is a two-element set {{a}, {a, b}}.

Cartesian product

Ordered n-tuple

Analogically, an ordered n-tuple ⟨x1, x2, . . . , xn⟩ is defined by ⟨⟨x1, x2, . . . , xn−1⟩, xn⟩.

Cartesian product for of n sets

Indexed family of sets.

What does I→2^X means in definition of indexed family

Family

set of sets

Generalized union

Generalized intersection (incorrect)

Double indexed family of sets

Disjoint sets

A∩B= ∅.

How much elements does power set 2^X have if X have N elements.

2^N