Ads
related to: integers and absolute value examplesThis site is a teacher's paradise! - The Bender Bunch
- Guided Lessons
Learn new concepts step-by-step
with colorful guided lessons.
- Digital Games
Turn study time into an adventure
with fun challenges & characters.
- Worksheet Generator
Use our worksheet generator to make
your own personalized puzzles.
- Printable Workbooks
Download & print 300+ workbooks
written & reviewed by teachers.
- Guided Lessons
Search results
Results from the WOW.Com Content Network
The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.
The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
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 ...
For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers.
Consider, for example, the integers. In addition to the usual absolute value function |·| : Q → R, there are p-adic absolute value functions |·| p : Q → R, defined for each prime number p, which measure divisibility by p. Ostrowski's theorem states that these are all possible absolute value functions on Q (up to equivalence).
The 3-adic integers, with selected corresponding characters on their Pontryagin dual group. In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; p-adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number p ...
When the ordered abelian group Γ is the additive group of the integers, the associated valuation is equivalent to an absolute value, and hence induces a metric on the field K. If K is complete with respect to this metric, then it is called a complete valued field .
The real numbers form a metric space: the distance between x and y is defined as the absolute value |x − y|. By virtue of being a totally ordered set, they also carry an order topology ; the topology arising from the metric and the one arising from the order are identical, but yield different presentations for the topology—in the order ...
Ads
related to: integers and absolute value examplesThis site is a teacher's paradise! - The Bender Bunch