7.NS.A.1.B Understand p + q as the number located a distance |q
... negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 1) Use absolute value to express in simplest form: | ...
... negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 1) Use absolute value to express in simplest form: | ...
Adding Integers
... Adding Integers with the Same Sign: ___________ the _______________ values of the numbers. Use the ___________ of the ___________________. Adding Integers with Different Signs: _________________ the absolute ______________ of the numbers. Use the __________ of the numbers with the greater __________ ...
... Adding Integers with the Same Sign: ___________ the _______________ values of the numbers. Use the ___________ of the ___________________. Adding Integers with Different Signs: _________________ the absolute ______________ of the numbers. Use the __________ of the numbers with the greater __________ ...
Dyadic Harmonic Analysis and the p-adic numbers Taylor Dupuy July, 5, 2011
... any Ultra metric space has a property of dyadic intevals that you are probably familiar with: Proposition 0.4. Let (X, d) be an Ultrametric space. For all balls B and B 0 we have B ∩ B 0 = ∅ or B ⊂ B 0 = ∅ or B 0 ⊂ B. Proof. Let B = Br (x) and B 0 = Br0 (x0 ). Without loss of generality we can assum ...
... any Ultra metric space has a property of dyadic intevals that you are probably familiar with: Proposition 0.4. Let (X, d) be an Ultrametric space. For all balls B and B 0 we have B ∩ B 0 = ∅ or B ⊂ B 0 = ∅ or B 0 ⊂ B. Proof. Let B = Br (x) and B 0 = Br0 (x0 ). Without loss of generality we can assum ...
2 Slides Per Page
... text, but it can be taught to students who are struggling to speed up their calculations. This is NOT, however, a substitute for these models, as students should have a deep understanding of whether the solution is positive or negative before learning these. 1. If you are adding two numbers wit ...
... text, but it can be taught to students who are struggling to speed up their calculations. This is NOT, however, a substitute for these models, as students should have a deep understanding of whether the solution is positive or negative before learning these. 1. If you are adding two numbers wit ...
The Value of the Number Line
... vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. ...
... vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. ...
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.