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In mathematics, a dual system, dual pair or a duality over a field is a triple (,,) consisting of two vector spaces, and , over and a non-degenerate bilinear map:. In mathematics , duality is the study of dual systems and is important in functional analysis .
The All-time Bundesliga table (German: Ewige Tabelle der Bundesliga) is a ranking of all German football clubs based on their performance in the Bundesliga, the top division of German football. In this ranking 3 points are awarded for a win, 1 for a draw, and 0 for a loss, although the Bundesliga awarded 2 points for a win until the 1994–95 ...
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In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form a + bε, where a and b are real numbers, and ε is a symbol taken to satisfy = with .
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
The all-time DDR-Oberliga table is a cumulative record of all match results, points, and goals of every team that played in the former East Germany's first division DDR-Oberliga [1] from its inception in 1949 until its dissolution in 1991 following German reunification.
A definition of a hypercomplex number is given by Kantor & Solodovnikov (1989) as an element of a unital, but not necessarily associative or commutative, finite-dimensional algebra over the real numbers.
Tabelle der wichtigsten Formeln aus der Differential-Rechnung, many editions Grundriss der Differential- und Integral-Rechnung , Helwing, Hannover, 2 vols., many editions [ 2 ] [ 3 ] Grundriss der Integral-Rechnung , 2 vols., many editions