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The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k). m is smoother than n if the largest prime factor of m is below the largest of n.
Examples of computer clip art, from Openclipart. Clip art (also clipart, clip-art) is a type of graphic art. Pieces are pre-made images used to illustrate any medium. Today, clip art is used extensively and comes in many forms, both electronic and printed. However, most clip art today is created, distributed, and used in a digital form.
The Math Images Project is a wiki collaboration between Swarthmore College, the Math Forum at Drexel University, and the National Science Digital Library. The project aims to introduce the public to mathematics through beautiful and intriguing images found throughout the fields of math. The Math Images Project runs on MediaWiki software, as ...
For example: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
Froebel star: November 2013: A line integral is an integral where the function to be integrated, be it a scalar field as here or a vector field, is evaluated along a curve.The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field ...
As 120 is a factorial and one less than a square (! =), it—with 11—is one of the few Brown number pairs. 120 appears in Pierre de Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that, when multiplied by any of the other numbers in the sequence ...
The only prime belonging to two pairs of cousin primes is 7. One of the numbers n, n + 4, n + 8 will always be divisible by 3, so n = 3 is the only case where all three are primes. An example of a large proven cousin prime pair is (p, p + 4) for = + which has 20008 digits.