Ordered pair

In mathematics, an ordered pair (a, b) is a pair of mathematical objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.)

Ordered pairs are also called 2-tuples, or sequences of length 2; ordered pairs of scalars are also called 2-dimensional vectors. The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as one pair nested in another.

In the ordered pair (a, b), the object a is called the first entry, and the object b the second entry of the pair. Alternatively, the objects are called the first and second coordinates, or the left and right projections of the ordered pair.

Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs.

A&B

A&B may refer to:

AB

AB, Ab, or ab may refer to:

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A. B. Dille

Avery B. Dille was an American football and basketball player, coach, and sports figure in the United States.

Playing history

Dille played halfback for the Mississippi A&M (now Mississippi State University) football team and was awarded a letter for the 1910 season.

Coaching history

Football

Dillie was the head coach of the Mississippi Normal college football program in Hattiesburg, Mississippi (now called "University of Southern Mississippi"). He held the position from 1914 until conclusion of the 1916 season and was the third person to hold the position at the school. His overall record at Southern Miss was 6 wins, 10 losses, and 1 tie. As of conclusion of the 2009 season, this ranks him 12th in terms of total wins at the school.

A unique positive turning point occurred in the 1916 season as the result of a loss. In what was called the program's "Greatest pre-World War I success" the team lost to Ole Miss by a score of 13 to 7. The school's leadership at the time took this as a sign that the program could compete nationally in the sport of football.