Section 1.1-1.3fill
... Same sign − just add the numbers and keep the sign Different signs – subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. ...
... Same sign − just add the numbers and keep the sign Different signs – subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. ...
Table 1 Fill in the blank: Choose a word from the bank below to fill in
... A non repeating, non terminating decimal represents a/an _______________. All whole number and their opposites are called ______________. _______________ is a whole number but NOT a natural number. Answer each question carefully. Be sure to show all work when appropriate. Circle the choice that show ...
... A non repeating, non terminating decimal represents a/an _______________. All whole number and their opposites are called ______________. _______________ is a whole number but NOT a natural number. Answer each question carefully. Be sure to show all work when appropriate. Circle the choice that show ...
Number System and Closure Notes
... 6. Name a number that is an integer but not a whole number. ________________ 7. Name a number that is rational but not a counting number. ________________ 8. Name a number that is whole but not counting. _______________________ 9. Name a number that is counting but not whole. ______________________ ...
... 6. Name a number that is an integer but not a whole number. ________________ 7. Name a number that is rational but not a counting number. ________________ 8. Name a number that is whole but not counting. _______________________ 9. Name a number that is counting but not whole. ______________________ ...
Real Numbers
... factorization is unique, apart from the order in which the prime factors occur. Ex. 28 = 2 x 2 x 7 ; 27 = 3 x 3 x 3 Theorem : Sum or difference of a rational and irrational number is irrational. Theorem : The product and quotient of a non-zero rational and irrational number is irrational. Theorem : ...
... factorization is unique, apart from the order in which the prime factors occur. Ex. 28 = 2 x 2 x 7 ; 27 = 3 x 3 x 3 Theorem : Sum or difference of a rational and irrational number is irrational. Theorem : The product and quotient of a non-zero rational and irrational number is irrational. Theorem : ...
Different Number Systems
... .6̄, for instance, is not an irrational number. Even though it has an infinite number of numbers after the decimal place, it can be expressed as the ratio of two integers. Namely, 2 and 3, as 23 = .6̄. If we start seeing patterns in the numbers following the decimal place that is a sign that the dec ...
... .6̄, for instance, is not an irrational number. Even though it has an infinite number of numbers after the decimal place, it can be expressed as the ratio of two integers. Namely, 2 and 3, as 23 = .6̄. If we start seeing patterns in the numbers following the decimal place that is a sign that the dec ...
1.5: Rational Numbers
... Ordering Rational Numbers The peaks of four mountains or seamounts are located either below or above sea level as follows: 1/4 mi, -0.2 mi, -2/9 mi, 1.1 mi. Put them in order from least to greatest please. ...
... Ordering Rational Numbers The peaks of four mountains or seamounts are located either below or above sea level as follows: 1/4 mi, -0.2 mi, -2/9 mi, 1.1 mi. Put them in order from least to greatest please. ...
Chapter 5.2 What does this goal mean you need to do? Show an
... N = the set of natural numbers W = the set of whole numbers I = the set of integers Q = the set of rational numbers ...
... N = the set of natural numbers W = the set of whole numbers I = the set of integers Q = the set of rational numbers ...
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.