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

Draw a common graph f ( x ) = |x|, Graph f ( x ) = |x| Solution The...

Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f

Cylindrical coordinate system, how to describe the locus of the equation x^...

how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?

Prove that a simple graph is connected, Prove that a simple graph is connec...

Prove that a simple graph is connected if and only if it has a spanning tree.    Ans: First assume that a simple graph G has a spanning  tree T.  T consists of every node of G.

Solve 5x tan (8x ) =3x trig function, Solve 5x tan (8x ) =3x . Solution...

Solve 5x tan (8x ) =3x . Solution : Firstly, before we even begin solving we have to make one thing clear.  DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like

Scaling and translation for equations, Q. Scaling and translation for equat...

Q. Scaling and translation for equations? Ans. If you have an equation in the form y= f(x) (if you're not familiar with functions, that just means having "y" on the left s

Children have their own strategies for learning maths, Children Have Their ...

Children Have Their Own Strategies For Learning Vibhor, aged 7, was once asked if he knew what 'seven lots of eight' are. He said he didn't. He was then asked, "Can you work it

Which of the subsequent binomials could represent the length, The area of a...

The area of a rectangle is represented through the trinomial: x 2 + x - 12. Which of the subsequent binomials could represent the length and width? Because the formula for the

Tangents, two circle of radius of 2cm &3cm &diameter of 8cm dram common tan...

two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent

Quantitative analysis, Suppose the economy is now ‘open’ and thus has an ex...

Suppose the economy is now ‘open’ and thus has an external demand (e.g. from the government, exports, etc.) of the dollar amounts for each respective industry. In the latest budget

Erin is painting a bathroom what is the area to be painted, Erin is paintin...

Erin is painting a bathroom along with four walls each measuring 8 ft through 5.5 ft. Ignoring the doors or windows, what is the area to be painted? The area of the room is the

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