Chapter 5: Rational Numbers as Fractions
... have been removed; we say that the numerator and the denominator are relatively prime when a fraction is in simplest form 5.1.1.10. lowest terms – same as simplest form 5.1.1.11. denseness – there are no holes in the number line, the number line is said to be dense because in between any two numbers ...
... have been removed; we say that the numerator and the denominator are relatively prime when a fraction is in simplest form 5.1.1.10. lowest terms – same as simplest form 5.1.1.11. denseness – there are no holes in the number line, the number line is said to be dense because in between any two numbers ...
Real Numbers PowerPoint
... ABSOLUTE VALUE • Always gives a positive answer or zero. • If there is arithmetic inside the absolute value symbol do that first, then take the absolute value of the answer. ...
... ABSOLUTE VALUE • Always gives a positive answer or zero. • If there is arithmetic inside the absolute value symbol do that first, then take the absolute value of the answer. ...
11-4 Sets
... A contains all the positive integers that are factors of 21, B is the set of multiples of 7 contained in U, C is the set of odd numbers contained in U. (a) List all the members of set A. ...
... A contains all the positive integers that are factors of 21, B is the set of multiples of 7 contained in U, C is the set of odd numbers contained in U. (a) List all the members of set A. ...
Essential Questions Understandings The student will understand
... vertical number line diagram. (7.NS.1) Use words, visuals and symbols to describe situations in which opposite quantities combine to make 0. (7.NS.1) Represent addition of quantities with symbols, visuals and words by showing positive or negative direction from one quantity to the other. (7.NS.1) Sh ...
... vertical number line diagram. (7.NS.1) Use words, visuals and symbols to describe situations in which opposite quantities combine to make 0. (7.NS.1) Represent addition of quantities with symbols, visuals and words by showing positive or negative direction from one quantity to the other. (7.NS.1) Sh ...
Quiz
... 3 qualifies since it is 3 / 1 , and –4, 1 / 2 , and 1 / 7 likewise also clearly qualify. Any terminating decimal is rational, as exemplified by 3.14 since it can be written as a ratio: ...
... 3 qualifies since it is 3 / 1 , and –4, 1 / 2 , and 1 / 7 likewise also clearly qualify. Any terminating decimal is rational, as exemplified by 3.14 since it can be written as a ratio: ...
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.