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The term absolute value has been used in this sense from at least 1806 in French [3] and 1857 in English. [4] The notation | x |, with a vertical bar on each side, was introduced by Karl Weierstrass in 1841. [5] Other names for absolute value include numerical value [1] and magnitude. [1]
Ostrowski's theorem states that the nontrivial places of the rational numbers Q are the ordinary absolute value and the p-adic absolute value for each prime p. [3] For a given prime p , any rational number q can be written as p n ( a / b ), where a and b are integers not divisible by p and n is an integer.
The absolute value of a real number r is defined by: [4] | | =, | | =, < Absolute value may also be thought of as the number's distance from zero on the real number line. For example, the absolute value of both 70 and −70 is 70.
The p-adic valuation is a valuation and gives rise to an analogue of the usual absolute value. Whereas the completion of the rational numbers with respect to the usual absolute value results in the real numbers R {\displaystyle \mathbb {R} } , the completion of the rational numbers with respect to the p {\displaystyle p} -adic absolute value ...
In number theory, Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers is equivalent to either the usual real absolute value or a p-adic absolute value. [1]
Hints and the solution for today's Wordle on Saturday, February 8.
From January 2008 to December 2012, if you bought shares in companies when Gail R. Wilensky joined the board, and sold them when she left, you would have a -5.2 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
The complex numbers of absolute value one form the unit circle. Adding a fixed complex number to all complex numbers defines a translation in the complex plane, and multiplying by a fixed complex number is a similarity centered at the origin (dilating by the absolute value, and rotating by the argument).