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

Determine the matrix that performs a horizontal compression, (a) Determine ...

(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi

the comic book, a) The first comic book is of shakitman was sold in 1938. ...

a) The first comic book is of shakitman was sold in 1938. In 2010, the estimated price for this comic book in good condition was about $500,000. This represented a return of 25 per

Diffrence between integers and rational numbers, Q. Give basic Diffrence be...

Q. Give basic Diffrence between Integers and Rational Numbers? Ans. Integers The integers are positive and negative whole numbers. The integers are closed under ad

Solve 4 sin 2 ( t ) - 3 sin ( t /3)= 1, Solve 4 sin 2 ( t ) - 3 sin ( t /...

Solve 4 sin 2 ( t ) - 3 sin ( t /3)= 1 . Solution Before solving this equation let's solve clearly unrelated equation. 4x 2 - 3x = 1  ⇒ 4x 2 - 3x -1 = ( 4x + 1) ( x

Evaluate the subsequent inverse trigonometric functions, Evaluate the subse...

Evaluate the subsequent inverse trigonometric functions: Evaluate the subsequent inverse trigonometric functions. arcsin   0.3746 22° arccos  0.3746 69° arctan  0.383

Complex number 1pi in polar form, Whlie solving complex number 1pi in polar...

Whlie solving complex number 1pi in polar form.In book they have taken theta =-pi/4 why not 7pi/4 because the point lie in fourth quadrant and the theta is given by 2pi-angle(alpha

Trignometry, prove that cos(a)/1-sin(a)=tan(45+A/2)

prove that cos(a)/1-sin(a)=tan(45+A/2)

Daily revenue for next 30 days, Owner of a computer repair shop has daily r...

Owner of a computer repair shop has daily revenue with mean $7200 and SD $1200 Daily revenue for next 30 days will be monitored. What is probability that daily revenue for those 30

Show that tan = 1/v3 , If 7sin 2 ?+3cos 2 ? = 4, show that tan? =   1/√3  ...

If 7sin 2 ?+3cos 2 ? = 4, show that tan? =   1/√3                      . Ans:    If 7 Sin 2 ? + 3 Cos 2 ? = 4 S.T. Tan?  1/√3 7 Sin 2 ? + 3 Cos 2 ? = 4 (Sin 2 ? + Cos 2 ?)

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