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

Venn diagram, in a class of 55 students, 35 take english, 40 take french, a...

in a class of 55 students, 35 take english, 40 take french, and 5 take other languages.present this information in a venn diagam and determine how many students take both languages

Fundamental theorem of integral facts , Fundamental Theorem of Calculus, Pa...

Fundamental Theorem of Calculus, Part II  Assume f(x) is a continuous function on [a,b] and also assume that F(x) is any anti- derivative for f(x). Hence, a ∫ b f(x) dx =

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

Parabola, please i need the answers to x^_7x+10 i want the vertex,axis of s...

please i need the answers to x^_7x+10 i want the vertex,axis of semetery,y intersect and the x intercept

One is then added to in which result what is final answer, Ten is decreased...

Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures

Working definition of continuity , "Working" definition of continuity ...

"Working" definition of continuity A function is continuous in an interval if we can draw the graph from beginning point to finish point without ever once picking up our penci

Conclude the values of the six trigonometric functions, Conclude the values...

Conclude the values of the six trigonometric functions: Conclude the values of the six trigonometric functions of an angle formed through the x-axis and a line connecting the

I Need Help, If 3200 sweets cost 30 US Dollars how much will 13,500 sweets ...

If 3200 sweets cost 30 US Dollars how much will 13,500 sweets cost ?

Integral calculus, how to change order and variable in multiple integral

how to change order and variable in multiple integral

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