Ordered Pair

Definition

An ordered pair is a two-part structure where order matters.

Example:

(a, b)

The first position is a.

The second position is b.

Ordered pair = two objects with position.

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Order Matters

These are not generally the same:

(a, b)
(b, a)

Example:

(person, city)

means something different from:

(city, person)

The same two objects appear, but their roles changed.

Position gives meaning in an ordered pair.

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Ordered Pair vs Set

A set does not care about order.

Example:

{a, b} = {b, a}

An ordered pair does care about order.

Example:

(a, b) is not the same as (b, a)

Sets ignore order; ordered pairs preserve order.

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Ordered Pairs In Relations

Relations are built from ordered pairs.

Example:

R = {(1, 2), (2, 3), (3, 4)}

Each pair records a connection.

For example:

(1, 2)

may mean:

1 points to 2

Ordered pairs are the basic units of relations.

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Final Summary

• An ordered pair has two positions.
• Order matters in an ordered pair.
• (a, b) is generally different from (b, a).
• Ordered pairs are different from sets.
• Relations are sets of ordered pairs.