chapter 6
... • For any real x (except 0), there is exactly one number on the number line that is the same distance from 0 but on the other side of x. This is the additive inverse, or opposite, of x. • The additive inverse of x is -x ...
... • For any real x (except 0), there is exactly one number on the number line that is the same distance from 0 but on the other side of x. This is the additive inverse, or opposite, of x. • The additive inverse of x is -x ...
Chapter 2-7
... Reminder: Natural Numbers = {1, 2, 3, …} Whole Numbers = {0, 1, 2, 3, …} Integers = {…, -2, -1, 0, 1, 2, …} Rational Numbers: a/b where b ≠ 0. The decimal form of a rational number is a terminating or repeating decimal. Irrational numbers: the decimal form of a irrational number is a non-terminating ...
... Reminder: Natural Numbers = {1, 2, 3, …} Whole Numbers = {0, 1, 2, 3, …} Integers = {…, -2, -1, 0, 1, 2, …} Rational Numbers: a/b where b ≠ 0. The decimal form of a rational number is a terminating or repeating decimal. Irrational numbers: the decimal form of a irrational number is a non-terminating ...
Rational Numbers
... • Repeating decimals can always be written as fractions, so repeating decimals are always rational numbers. You can use bar notation to indicate that some part of a decimal repeats forever, for example, 0.333… 0.3 ...
... • Repeating decimals can always be written as fractions, so repeating decimals are always rational numbers. You can use bar notation to indicate that some part of a decimal repeats forever, for example, 0.333… 0.3 ...
Introduction to Integers
... opposites (positive or negative) additive inverse- the sum of a number and its opposite absolute value- the distance of a number from zero on a number line; shown by l l ...
... opposites (positive or negative) additive inverse- the sum of a number and its opposite absolute value- the distance of a number from zero on a number line; shown by l l ...
STUDY GUIDE FOR INVESTIGATIONS 1 AND 2
... Problem 1.4 Goal: to understand addition and subtraction of integers through the use of a chipboard model. Red chips represent negative numbers Black chips represent positive numbers One red chip and one black chip = 0 and are called a Zero Pair Any number of zero pairs may be added to the c ...
... Problem 1.4 Goal: to understand addition and subtraction of integers through the use of a chipboard model. Red chips represent negative numbers Black chips represent positive numbers One red chip and one black chip = 0 and are called a Zero Pair Any number of zero pairs may be added to the c ...
1-2
... **Every rational number that is not an integer can be written as a fraction. 1. A common fraction is written with a _____________ and ____________. 2. Even decimals can be converted into fractions. 3. _____________ decimals are decimals with a finite number of ...
... **Every rational number that is not an integer can be written as a fraction. 1. A common fraction is written with a _____________ and ____________. 2. Even decimals can be converted into fractions. 3. _____________ decimals are decimals with a finite number of ...
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.