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

Calculus, What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at t...

What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at the point (4, f(4))

Find the sum of all natural no. between 101 and 304, Find the sum of all na...

Find the sum of all natural no. between 101 & 304 which are divisible by 3 or 5. Find their sum. Ans:    No let 101 and 304, which are divisible by 3. 102, 105..........

Geometric mean-geometric progression, Geometric mean - It is a measure ...

Geometric mean - It is a measure of central tendency normally utilized to measure industrial increases rates. - It is explained as the nth root of the product of 'n' observa

Hyperbolic paraboloid- three dimensional space, Hyperbolic Paraboloid- Thre...

Hyperbolic Paraboloid- Three Dimensional Space The equation which is given here is the equation of a hyperbolic paraboloid. x 2 / a 2 - y 2 / b 2 = z/c Here is a dia

Order of Operations with Fractions, 1.)3 3/8 divided by 4 7/8 plus 3 2.)4 ...

1.)3 3/8 divided by 4 7/8 plus 3 2.)4 1/2 minus 3/4 divided by 2 3/8

Rounding, the number is 605176 the underline digit is 0

the number is 605176 the underline digit is 0

Computerised payroll package, How to calculate costs if you have a computer...

How to calculate costs if you have a computerised payroll package for your large business?

Linear equations in one variable, three prices are to be distributed in a q...

three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of

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