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

Retest Simulation, What is the probability of guessing five questions on a ...

What is the probability of guessing five questions on a test correctly

Transportation problem, matlab code for transportation problem solved by vo...

matlab code for transportation problem solved by vogel''s approximation method

1, use 3/8 of a thin of paint, what fraction of the paint is left in thin (...

use 3/8 of a thin of paint, what fraction of the paint is left in thin (show work

Solve for, a)Solve for ?, if tan5? = 1. Ans:    Tan 5? = 1        ⇒ ? ...

a)Solve for ?, if tan5? = 1. Ans:    Tan 5? = 1        ⇒ ? =45/5 ⇒ ?=9 o . b)Solve for ? if S i n ?/1 + C os ? + 1 +  C os ?/ S i n ? = 4 . Ans:  S i n ?/1 +

Find an example of congruential unit random number generator, 1. Suppose th...

1. Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables

Define number line, Q. Define Number Line? Ans. A number line is a...

Q. Define Number Line? Ans. A number line is a nice way to visualize and examine the ordering of the positive and negative numbers. Every positive and negative number that

Find least number of cables required to connect 100 computer, Find out the ...

Find out the least number of cables required to connect 100 computers to 20 printers to assurance that 20 computers can directly access 20 different printers.  Justify your answer.

Initial value problems, Write a Matlab function MyIVP that solves an initia...

Write a Matlab function MyIVP that solves an initial-value problem (IVP) for a system of ordinary differential equations (ODEs) of the form x ?(t) = f (t, x(t)), where f : R × Rn ?

Evaluate following limits at infinity, Evaluate following limits. ...

Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc

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