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Unit A: Real Numbers - myLearning | Pasco County Schools
Unit A: Real Numbers - myLearning | Pasco County Schools



The Real Numbers
The Real Numbers

... infinity in both directions. However, to make any sense of this, we must label all the points on this line and determine the relationship between them from different points of view. First, the real numbers form an algebraic object known as a field, meaning that one may add, subtract, and multiply re ...
Exploring Integers - Bishop Alemany High School
Exploring Integers - Bishop Alemany High School

Irrationality measures for some automatic real numbers
Irrationality measures for some automatic real numbers

Algebra - New Age International
Algebra - New Age International

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1 Number Systems

Cognitive Models for Number Series Induction Problems
Cognitive Models for Number Series Induction Problems

Whole Numbers
Whole Numbers

2-1
2-1

online page proofs
online page proofs

... 62 Maths Quest 11 MATHEMATICAL METHODS VCE Units 1 and 2 ...
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1 lesson plan vi class

Math 7 Notes – Unit 02 Part B: Rational Numbers
Math 7 Notes – Unit 02 Part B: Rational Numbers

What are rational numbers?
What are rational numbers?

Algebraic foundations
Algebraic foundations

Math 7 Notes – Unit 01: Integers
Math 7 Notes – Unit 01: Integers

Grade 7 Module 2 Lessons 1–23 Eureka Math
Grade 7 Module 2 Lessons 1–23 Eureka Math

Grade 8 Rational Numbers
Grade 8 Rational Numbers

... In order to solve this expression, we will have to f ollow the correct precedence of operators i.e. Division, Multiplication, Addition and Subtraction (in that order). Step 2 Now, 4 + 5 × 9 - 7 + 322 ÷ 91 can be solved as: ...
Chapter4p1
Chapter4p1

Standard 1 - Briar Cliff University
Standard 1 - Briar Cliff University

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PAC EC CCSS Side-by-Side: Grade 6
PAC EC CCSS Side-by-Side: Grade 6

consecutive integers - Algebra 1 -
consecutive integers - Algebra 1 -

< 1 2 3 4 5 6 7 8 9 ... 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.
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