Real Number - 2716 Words

In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and Ï€ (3.14159265..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a†¦show more content†¦More formally, real numbers have the two basic properties of being an ordered field, and having the least upper bound property. The first says that real numbers comprise a field, with addition and multipli cation as well as division by nonzero numbers, which can be totally ordered on a number line in a way compatible with addition and multiplication. The second says that if a nonempty set of real numbers has an upper bound, then it has a least upper bound. The second condition distinguishes the real numbers from the rational numbers: for example, the set of rational numbers whose square is less than 2 is a set with an upper bound (e.g. 1.5) but no least upper bound: hence the rational numbers do not satisfy the least upper bound property. In physics In the physical sciences, most physical constants such as the universal gravitational constant, and physical variables, such as position, mass, speed, and electric charge, are modeled using real numbers. In fact, the fundamental physical theories such as classical mechanics, electromagnetism, quantum mechanics, general relativity and the standard model are described using mathematical structures, typically smooth manifolds or Hilbert spaces, that are based on the real numbers although actual measurements of physical quantities are ofShow MoreRelatedThe Distributive Property of Algebraic Expressions806 Words   |  4 PagesDistributive property of Algebraic expressions Janet Mency MAT 221 Instructor: Amy Glidewell January 25, 2014 Completing algebra problems can be difficult if you don’t understand the properties of real numbers. There are several properties in algebra dealing with both integers and real numbers; one that will be the focus of this report will be the distributive property. We use this property when we are combining addition and multiplication in an algebraic expression. Let’s say that you areRead MoreUnit 4707 Words   |  3 Pagesvariable to accept an Integer argument. The module should prompt the user to enter a number and then store the input in the reference parameter variable. Module getNumber (Integer Ref value) Display â€Å"Display a number† Input number End Module Module main ( ) Declare Integer x = 1 Declare Real y = 3.4 Display x, â€Å" â€Å", y Call changeUs (x, y) Display x, â€Å" â€Å",y End module Module changeUs (Integer a, Real b) Set a = 0 Set b = 0 Display a, â€Å" â€Å", b End Module It will not displayRead MoreNotes On Integers And Integers Essay736 Words   |  3 Pages3 NUMBERS Real Numbers: Real numbers are all numbers that can be represented in a number line. Natural Numbers: Natural numbers are all counting numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, †¦ Whole Numbers: Whole numbers are all positive numbers and zero such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, †¦ Integers: Integers are all positive and negative numbers and zero such as †¦-12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, †¦ Rational Numbers:Read More4.0 Student Essay618 Words   |  3 Pagesthe steps. The first step will always be to remove the parenthesis, which uses the distributive property. Second will always be combining like terms and adding related coefficients what we have been working on this week which is dealing with real numbers. Here is the solution to the first problem: 2a(a-5)+ 4(a-5) =2aa+2a(-5)+4a-4â‹…5 =2a^2-10a+4a-20 =2a^2-6a-20 The steps used to simplify this equation are as follows: First I remove all of the parentheses. This is called the distributiveRead MorePt1420 Assignment Essay1063 Words   |  5 PagesA posttest loop means it performs an iteration before testing its condition 3) What is a condition-controlled loop? A condition-controlled loop uses a true/false condition to control the number of times that it repeats 4) What is a count-controlled loop? A count-controlled loop repeats a specific number of times 5) What three actions do count-controlled loops typically perform using the counter variable? 1) Initialization: the variable is initialized 2) Test: the loop tests the variable byRead MoreMathematical Reasoning And Technical Reasoning1136 Words   |  5 PagesUnderstanding the similarities and differences amongst the four operations provides flexibility when solving word problems. â€Å"As children develop their understanding of the operations, they should simultaneously be developing more sophisticated ideas about numbers† (Van de Walle, Karp, Bay-Williams, 2013). To successfully perform mathematical tasks involving any operation, students must understand their relation. Students must realize that addition and subtraction share similar vocabulary. For example, bothRead MoreEssay on WK 3 Assignment735 Words   |  3 Pagesï » ¿ Real World Radical Formulas MAT222:  Intermediate  Algebra Instructor Peter Surgent August 31, 2014 Real World Radical Formulas Radical formulas are used in many fields of the real world; some examples are in finance, medicine, engineering, and physics. These are just a few.  In the finance department they use  it to find the interest, depreciation and compound interests.  In medicine it can be used to calculate the Body Surface of an adult (BSA), in engineering it  can be usedRead MoreThe National Library Of Virtual Manipulatives997 Words   |  4 Pageslearners. The portal gives support for all types of mathematics models through the usage of collaborative activities. 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To find theRead MoreMechanisms of Using Numbers in Computer Engineering527 Words   |  2 Pagesworking with numbers is one of the most substantial concepts. Numbers are not used only in civil or architecture engineering as most of people think. Numbers are important in all engineering disciplines. For example, agriculture engineers work in numbers in there calculation to design systems that produce food, feed, fiber and other products with high quality. Also, in computer engineering field, computer engineers must know how to deal with numbers because computer language based on numbers. For this