• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
PDF
PDF

Some Conjectures About Cyclotomic Integers
Some Conjectures About Cyclotomic Integers

... If we consider instead the closed interior of the unit circle, \ z\ ^ 1, then we allow only one additional algebraic integer, namely 0. But if we consider the set | z | |Ä, where R > 1, then infinitely many other algebraic integers appear. Indeed, by a theorem of Fekete and Szegö [1], there are infi ...
notes on rational and real numbers
notes on rational and real numbers

Computing with Floating Point Numbers
Computing with Floating Point Numbers

A UNIFORM OPEN IMAGE THEOREM FOR l
A UNIFORM OPEN IMAGE THEOREM FOR l

RNS3 REAL NUMBER SYSTEM
RNS3 REAL NUMBER SYSTEM

THE p-ADIC EXPANSION OF RATIONAL NUMBERS 1. Introduction
THE p-ADIC EXPANSION OF RATIONAL NUMBERS 1. Introduction

Grade 6 Integers
Grade 6 Integers

On the expansions of a real number to several integer bases Yann
On the expansions of a real number to several integer bases Yann

(Unit 1) Operations with Rational Numbers - Grubbs
(Unit 1) Operations with Rational Numbers - Grubbs

THE NUMBER SYSTEM
THE NUMBER SYSTEM

Why Is the 3X + 1 Problem Hard? - Department of Mathematics, CCNY
Why Is the 3X + 1 Problem Hard? - Department of Mathematics, CCNY

Rational and Irrational Numbers
Rational and Irrational Numbers

Rational and Irrational Numbers
Rational and Irrational Numbers

Resource 6A1.1 - Uniservity CLC
Resource 6A1.1 - Uniservity CLC

... Objective: Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line Write on the board five or six numbers with two decimal places, such as 3.46, 4.06, 12.76, 8.60, 11.18. Ask children to read each ...
Real Numbers and Monotone Sequences
Real Numbers and Monotone Sequences

Full text
Full text

Grade 6 Integers - multiple multiplication operations
Grade 6 Integers - multiple multiplication operations

... Multiplication of 15 negative numbers and 4 positive numbers, = (Multiplication of 15 negative numbers) × (Multiplication of 4 positive numbers) = (Multiplication of 14 negative numbers) × (Negative number) × (Multiplication of 4 positive numbers) = (Positive number) × (Negative number) × (Positive ...
PPT
PPT

Rational Numbers Grade 8
Rational Numbers Grade 8

The Rational Numbers
The Rational Numbers

- Triumph Learning
- Triumph Learning

... are natural numbers and their opposites and 0. a , where a and b are Rational numbers are numbers that can be expressed in the form __ b integers and b  0. Rational numbers include positive and negative fractions, mixed numbers, improper fractions, terminating decimals, and repeating decimals. ...
1.6 Division of Rational Numbers
1.6 Division of Rational Numbers

Full text
Full text

Course 2 Student Text Chapter 4
Course 2 Student Text Chapter 4

< 1 2 3 4 5 6 7 8 9 10 ... 53 >

P-adic number



In mathematics the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of ""closeness"" or absolute value. In particular, p-adic numbers have the interesting property that they are said to be close when their difference is divisible by a high power of p – the higher the power the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.p-adic numbers were first described by Kurt Hensel in 1897, though with hindsight some of Kummer's earlier work can be interpreted as implicitly using p-adic numbers. The p-adic numbers were motivated primarily by an attempt to bring the ideas and techniques of power series methods into number theory. Their influence now extends far beyond this. For example, the field of p-adic analysis essentially provides an alternative form of calculus.More formally, for a given prime p, the field Qp of p-adic numbers is a completion of the rational numbers. The field Qp is also given a topology derived from a metric, which is itself derived from the p-adic order, an alternative valuation on the rational numbers. This metric space is complete in the sense that every Cauchy sequence converges to a point in Qp. This is what allows the development of calculus on Qp, and it is the interaction of this analytic and algebraic structure which gives the p-adic number systems their power and utility.The p in p-adic is a variable and may be replaced with a prime (yielding, for instance, ""the 2-adic numbers"") or another placeholder variable (for expressions such as ""the ℓ-adic numbers""). The ""adic"" of ""p-adic"" comes from the ending found in words such as dyadic or triadic, and the p means a prime number.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report