Defining real numbers, Mathematics

Assignment Help:

The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers.

Another definition of real numbers uses a concept called number line (we will learn about it shortly). According to this definition a real number is any number that is the co-ordinate of the point on a real number line.

Sets of real numbers and relations among such sets can often be visualized by the use of a number line or co-ordinate axis. A number line is constructed by fixing a point O called the origin and another point U called the unit point on a horizontal straight line L. It is shown below. Therefore, on a number line we observe that positive numbers are in the increasing order as we move to the right of the origin whereas the negative numbers are in the decreasing order as we move to the left of the origin.

166_real numbers.png

Each point P on the line L is now assigned a "numerical address" or co-ordinate "x" representing its distance from the origin, measured in terms of the given unit. Thus x = +-d, where d is the distance between O and P (shown above). The plus sign or minus sign is used to indicate whether P is to the right of the origin or to the left of the origin. If the resulting number line is drawn to some scale, each point P has a corresponding numerical value and to each real numerical value "x" there will be corresponding unique point P on the number line. This can be observed on the number line. In other words for a point say 3.7, there is only a single point on the number line and for a point Q there will be unique numerical value. 


Related Discussions:- Defining real numbers

Set theory, how to prove Decidability Theorem of Logic

how to prove Decidability Theorem of Logic

Venn diagram, A venn diagram is a pictorial representation of the sam...

A venn diagram is a pictorial representation of the sample space of an experiment. It is usually drawn as a rectangular figure representing the sample space and it cont

Discount, outdoor grill- regular price:$360 discount:33 1/3%

outdoor grill- regular price:$360 discount:33 1/3%

Natural numbers, To begin with we have counting numbers. These ...

To begin with we have counting numbers. These numbers are also known as natural numbers and are denoted by a symbol 'N'. These numbers are obtai

Assemble the coefficient matrix and solve the linear system, Solve discrete...

Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length

Evaluate the volume of one orange, An orange has a diameter of 3 inches. Ev...

An orange has a diameter of 3 inches. Evaluate the volume of one orange. (π = 3.14) a. 9.42 in 3 b. 113.04 in 3 c. 28.26 in 3 d. 14.13 in 3 d. To determine the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd