What are p-adic numbers used for?

What are p-adic numbers used for?

The p-adic absolute value gives us a new way to measure the distance between two numbers. The p-adic distance between two numbers x and y is the p-adic absolute value of the number x-y. So going back to the 3-adics, that means numbers are closer to each other if they differ by a large power of 3.

What are p-adic groups?

In mathematics, the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

Are p-adic numbers a field?

For p any prime number, the p-adic numbers (or p-adic rational numbers, for emphasis) form a field ℚp that completes the field of rational numbers with respect to a metric, called the p-adic metric. As such they are analogous to real numbers.

Are p-adic numbers complete?

The reals and the p-adic numbers are the completions of the rationals; it is also possible to complete other fields, for instance general algebraic number fields, in an analogous way. This will be described now. Completing with respect to this absolute value | .

What is the p-adic metric?

What is the meaning of ADIC?

Adic definition (mathematics computing) When combined with prefixes derived (usually) from Latin or Greek names for numbers, used to make adjectives meaning “having a certain number of arguments” (said of functions, relations, etc, in mathematics and functions, operators, etc, in computing).

Is algebraic geometry useful in physics?

“Whereas with Einstein it was differential geometry that was the most relevant, for modern theoretical physics it is algebraic geometry. Algebraic geometry is the central aspect of geometry for the physicists now.”

Is geometric algebra useful?

Geometric algebra has been advocated, most notably by David Hestenes and Chris Doran, as the preferred mathematical framework for physics. Proponents claim that it provides compact and intuitive descriptions in many areas including classical and quantum mechanics, electromagnetic theory and relativity.

Are the P Adics a field?

A p-adic field is a finite field extension of Qp. If K is such a field, we denote by OK the ring of integers in K (that is, the integral closure of Zp in K). It is easy to see that since every element u ∈ K is algebraic over Qp, there is a ∈ Zp such that au ∈ OK.

What does ADIC mean in math?

having a certain number of arguments
Adic definition (mathematics computing) When combined with prefixes derived (usually) from Latin or Greek names for numbers, used to make adjectives meaning “having a certain number of arguments” (said of functions, relations, etc, in mathematics and functions, operators, etc, in computing). suffix.

Are P Adics a field?

What is NYO in government?

Not Yet Out. NYO. New York Offstage (New York, NY) Copyright 1988-2018 AcronymFinder.com, All rights reserved.

What is modern algebraic geometry about?

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

Is geometry a calculus?

Calculus vs Geometry Calculus is study of change while geometry is study of shapes. Geometry is much older than calculus. Calculus involves studying small change in an infinitesimal small quantity while geometry involves resolution of co-ordinates of a figure in dimensions.

What does CB mean in government?

CB Government Abbreviation

What is the application of algebraic geometry?

Applications. Algebraic geometry now finds applications in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling. There are also connections to string theory, game theory, graph matchings, solitons and integer programming.