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Nine is the number of derangements of 4, or the number of permutations of four elements with no fixed points. [8] 9 is the fourth refactorable number, as it has exactly three positive divisors, and 3 is one of them. [9] A number that is 4 or 5 modulo 9 cannot be represented as the sum of three cubes. [10]
The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.
The case = is the case of commutative finite fields; the nine element example above is =, =. In the seven exceptional examples, A {\displaystyle A} is of the form C p 2 {\displaystyle C_{p}^{2}} . This table, including the numbering by Roman numerals, is taken from Zassenhaus's paper.
The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.The snake lemma is valid in every abelian category and is a crucial tool in homological algebra and its applications, for instance in algebraic topology.
The concept of projection in mathematics is a very old one, and most likely has its roots in the phenomenon of the shadows cast by real-world objects on the ground. This rudimentary idea was refined and abstracted, first in a geometric context and later in other branches of mathematics. Over time different versions of the concept developed, but ...
For example, 90% would be described as "one nine"; 99% as "two nines"; 99.9% as "three nines"; and so forth. However, there are different conventions for representing inexact multiples of 9. For example, a percentage of 99.5% could be expressed as "two nines five" (2N5, or N2.5) [ 2 ] or as 2.3 nines, [ citation needed ] following from the ...
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Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
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