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A Hasse diagram is a simple picture of a finite partially ordered set, forming a drawing of the partial order's transitive reduction. Concretely, one represents each element of the set as a vertex on the page and draws a line segment or curve that goes upward from x to y precisely when x < y and there is no z such that x < z < y.
2. Double factorial: if n is a positive integer, n!! is the product of all positive integers up to n with the same parity as n, and is read as "the double factorial of n". 3. Subfactorial: if n is a positive integer, !n is the number of derangements of a set of n elements, and is read as "the subfactorial of n". *
The form α is defined by specifying, at each y ∈ N, how γ pairs with each k-vector v at y, and the value of that pairing is an integral over f −1 (y) that depends only on α, v, and the orientations of M and N. More precisely, at each y ∈ N, there is an isomorphism
meaning to add b and c first and then subtract the result from a, which would be written more commonly today as a − (b + c). Parentheses, used for grouping, are only rarely found in the mathematical literature before the eighteenth century. The vinculum was used extensively, usually as an overline, but Chuquet in 1484 used the underline ...
Möbius μ function: Sum of the nth primitive roots of unity, it depends on the prime factorization of n. Prime omega functions; Chebyshev functions; Liouville function, λ(n) = (–1) Ω(n) Von Mangoldt function, Λ(n) = log p if n is a positive power of the prime p; Carmichael function
Alt – alternating group (Alt(n) is also written as A n.) A.M. – arithmetic mean. AP – arithmetic progression. arccos – inverse cosine function. arccosec – inverse cosecant function. (Also written as arccsc.) arccot – inverse cotangent function. arccsc – inverse cosecant function. (Also written as arccosec.) arcexc – inverse ...
Mathematical ASCII Notation how to type math notation in any text editor. Mathematics as a Language at Cut-the-Knot; Stephen Wolfram: Mathematical Notation: Past and Future. October 2000. Transcript of a keynote address presented at MathML and Math on the Web: MathML International Conference.
For example, [] is the smallest subring of C containing all the integers and ; it consists of all numbers of the form +, where m and n are arbitrary integers. Another example: Z [ 1 / 2 ] {\displaystyle \mathbf {Z} [1/2]} is the subring of Q consisting of all rational numbers whose denominator is a power of 2 .
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