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The following table lists the names of small numbers used in the long and short scales, along with the power of 10, engineering notation, and International System of Units (SI) symbols and prefixes. [1] [page needed] [2] [page needed] [3] [page needed] [4] [5] [6] [7]
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
An example is the function that relates each real number x to its square x 2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x"). In this example, if the input is −3, then the output is 9, and we may write f(−3) = 9. The input variable(s) are sometimes referred to as the argument(s) of the function.
Guy gives Moser's circle problem as an example. The number of points (n), chords (c) and regions (r G). The first five terms for the number of regions follow a simple sequence, broken by the sixth term. Guy also formulated a second strong law of small numbers: When two numbers look equal, it ain't necessarily so! [3]
The tendency for an initial segment of data to show some bias that drops out later, one example in number theory being Kummer's conjecture on cubic Gauss sums The strong law of small numbers , an observation made by the mathematician Richard K. Guy: "There aren't enough small numbers to meet the many demands made of them."
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A property of weird numbers is that if n is weird, and p is a prime greater than the sum of divisors σ(n), then pn is also weird. [4] This leads to the definition of primitive weird numbers: weird numbers that are not a multiple of other weird numbers (sequence A002975 in the OEIS). Among the 1765 weird numbers less than one million, there are ...
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