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

What price tag will he put on the item, The manager of a specialty store ma...

The manager of a specialty store marks up imported products 110%. If a vase imported from Italy costs him $35, what price tag will he put on the item? To ?nd out the price he s

Example of the commutative property of addition, Tori was asked to provide ...

Tori was asked to provide an example of the commutative property of addition. Which of the subsequent choices would be correct? Using the simple interest formula Interest = pr

Steps for radio test - sequences and series, Steps for Radio test Assum...

Steps for Radio test Assume we have the series ∑a n Define, Then, a. If L b. If L>1 the series is divergent. c. If L = 1 the series might be divergent, this i

Division of complex number, Division of complex number Now, we gave thi...

Division of complex number Now, we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so let's look at a couple of e

What will the day of the week be the further time at the gym, Max goes to t...

Max goes to the gym every fourth day. Ellen's exercise routine is to go every third day. Today is Monday and both Max and Ellen are at the gym. What will the day of the week be the

The distributive law, The Distributive Law :  If you were asked to mentall...

The Distributive Law :  If you were asked to mentally multiply 37 with 9, how would you proceed? 1 would do it as follows - 37 is 30 + 7, 30 x 9 = 270, 7 x 9 = 63, so 270 + 63, th

What is the length of one side of the square, The area of a square is 64 cm...

The area of a square is 64 cm 2 . What is the length of one side of the square? To find out the area of a square, you multiply the length of a side through itself, because all

Show that a, If the roots of the equation (b-c)x 2 +(c-a)x +(a-b) = 0 are ...

If the roots of the equation (b-c)x 2 +(c-a)x +(a-b) = 0 are equal show that a, b, c are in AP. Ans:    Refer sum No.12 of Q.E. If (b-c)x 2 + (c-a) x + (a-b) x have equ

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