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

Grouping-categories of situations requiring division , Grouping - situatio...

Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t

., There are k baskets and n balls. The balls are put into the baskets rand...

There are k baskets and n balls. The balls are put into the baskets randomly. If k

Step functions, Before going to solving differential equations we must see ...

Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve

Show that aq= 1/2 perimeter of triangle abc, A circle touches the side BC o...

A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans:    Since the length o

Difererntial equation, Ask queFind the normalized differential equation whi...

Ask queFind the normalized differential equation which has {x, xex} as its fundamental setstion #Minimum 100 words accepted#

Bob is 2 years from being double as old as ellen, Bob is 2 years from being...

Bob is 2 years from being double as old as Ellen. The sum of twice Bob's age and three times Ellen's age is 66. How old is Ellen? Let x = Ellen's age and let y = Bob's age. Sin

Show that x(q-r) + y(r-p) + z(p-q) = 0, If the p th , q th & r th term of...

If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans:    p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (

Find the number., There is a number. If the sum of digits is 14, and if 29 ...

There is a number. If the sum of digits is 14, and if 29 is subtracted from the number, the digits become equal. Find the number.

Comperised payrolll package, a computerized payroll package and its cost,fu...

a computerized payroll package and its cost,futures and the size of the business and how business mathematics is an inbuilt component of the package

Statisctics, I would like to know what a symbol in my homework means?

I would like to know what a symbol in my homework means?

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