What is an ordered pair?

An ordered pair is a pair of objects, where the order in which the objects appear is significant. It is typically written as (a, b), where 'a' is the first element and 'b' is the second element.

• Significance of Order: The fundamental characteristic of an ordered pair is that (a, b) is considered different from (b, a) unless a = b. This distinguishes it from sets, where order doesn't matter.
• Applications: Ordered pairs are used extensively in mathematics and computer science. They can represent coordinates in a Cartesian coordinate system, relationships between sets, or inputs and outputs of functions.
• Equality: Two ordered pairs (a, b) and (c, d) are equal if and only if a = c and b = d.
• Examples:
  • In geometry, (3, 4) could represent a point on a 2D plane.
  • In relations, (Alice, Bob) could indicate a relationship from Alice to Bob.

In essence, an ordered pair is a foundational concept for representing relationships and locations where the sequence of elements is crucial.