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Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
In linear algebra, a vector space is an algebraic structure that allows for adding any two vectors and for scaling vectors. A familiar vector space is the set of all ordered pairs of real numbers; the ordered pair ( a , b ) is interpreted as a vector from the origin in the Euclidean plane to the point ( a , b ) in the plane.
Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures.For example, geometry has its origins in the calculation of distances and areas in the real world; algebra started with methods of solving problems in arithmetic.
The ten digits of the Arabic numerals, in order of value. A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10.
← 0 10 20 30 40 50 60 70 80 90 ... is 27-dimensional; [5] its automorphism group is the 52-dimensional exceptional Lie algebra. [6] There are twenty-seven ...
← 0 10 20 30 40 50 60 70 80 90 ... Abstract algebra. 92 is the total number of objects that are permuted by the series of five finite, simple Mathieu groups ...
The above arguments hold in any ring, a concept of abstract algebra generalizing integers and real numbers. [1]: p.48 0, 1, −1, i, and − i in the complex or Cartesian plane. Although there are no real square roots of −1, the complex number i satisfies i 2 = −1, and as such can be considered as a square root of −1. [2]
← 0 10 20 30 40 50 60 70 80 90 ... The octonions are a hypercomplex normed division algebra that are an extension of the complex numbers.
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