Columbus State Community College
... To write a negative number, put a negative sign (a dash) in front of it: –12. Notice that the negative sign looks exactly like the subtraction sign, as in 7 – 2 = 5. The negative sign and subtraction sign do not mean the same thing (more on that in the next section). To avoid confusion for now, we w ...
... To write a negative number, put a negative sign (a dash) in front of it: –12. Notice that the negative sign looks exactly like the subtraction sign, as in 7 – 2 = 5. The negative sign and subtraction sign do not mean the same thing (more on that in the next section). To avoid confusion for now, we w ...
1.1 The Real Numbers
... Note that for 52, where the exponent is 2 and the base is 5, not 5. So that 52 means: 52 = (52), and is read as “the opposite of 5 to the second, or 5 squared.” ...
... Note that for 52, where the exponent is 2 and the base is 5, not 5. So that 52 means: 52 = (52), and is read as “the opposite of 5 to the second, or 5 squared.” ...
Chapter 2 Lesson 2 Adding Integers pgs. 64-68
... but different signs • Additive Inverse (66): an integer and it’s opposite ...
... but different signs • Additive Inverse (66): an integer and it’s opposite ...
Lecture 2: Section 1.2: Exponents and Radicals Positive Integer
... 16 = 4 because 42 = 16 and 4 > 0. For a real number a, and a positive integer n, we define a1/n in a similar way a1/n = b ...
... 16 = 4 because 42 = 16 and 4 > 0. For a real number a, and a positive integer n, we define a1/n in a similar way a1/n = b ...
MODULE 19 Topics: The number system and the complex numbers
... Between any two irrational numbers there is a rational number because we can approximate any irrational number by a rational number from above or below. Theorem: All the rational numbers on the interval [0, 1] can be covered with open intervals such that the sum of the length of these intervals is a ...
... Between any two irrational numbers there is a rational number because we can approximate any irrational number by a rational number from above or below. Theorem: All the rational numbers on the interval [0, 1] can be covered with open intervals such that the sum of the length of these intervals is a ...
Topic for today: The irrational side of numbers How many rational
... A rational number x is one that can be written in the form x= ...
... A rational number x is one that can be written in the form x= ...
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.