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

The distributive law, The Distributive Law :  If you were asked to mentall...

The Distributive Law :  If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th

Find out the x-intercepts, Find out the x-intercepts & y-intercepts for eac...

Find out the x-intercepts & y-intercepts for each of the following equations.                            y =x 2 +x - 6 Solution As verification for each of these we wil

Triple integral transformed, An elliptical galaxy has gravitational boundar...

An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio

Word problem, mark got 15.00 for his birthday he now has 27.00. how much di...

mark got 15.00 for his birthday he now has 27.00. how much did he start with

Ratios, in a veggie mix the ratio of cups of carrots to cups of broccolie i...

in a veggie mix the ratio of cups of carrots to cups of broccolie is 4 to 5 if you made this party mix larger how many cups of carrots would be needed to mix with fo cups of brocco

Solid, The lateral edge of a pyramidal church spire is 61feet.Each side of ...

The lateral edge of a pyramidal church spire is 61feet.Each side of its octagonal base is 22feet. What will be the cost of painting the spire at 2.5 cents a square foot

Marketing of herbal products , To help Himalya herbal launch a successful m...

To help Himalya herbal launch a successful marketing campaign in the UK

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

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