Thursday, September 6, 2012

Different Sets of Real Numbers

Introduction to different set of real numbers
Different set of real numbers are those which comprise of both, rational numbers like 34, -23/149 and irrational numbers like v4, 2.45655. This means the different set of real numbers consist of integers both positive and negative, fractions and decimal expansions that may or may not replicate.

A set can be defined as a collection of objects. The sets we are talking about in this pamphlet are based on real numbers. Any object that is present in the set can be termed as an element/member of the set of real numbers. Sets are represented by Capital letters like A,B,C etc or also by brackets like {…..} hemming in symbols for the elements that are present in the set.

I.e.  {1, 2, 3, 4}. This means the elements of the set are 1,2,3,4.

Keep in mind that two sets are known to be equal only if the elements in each of the sets are the same.



Real numbers can be marked on the number line, making it much easier to picture and understand.

I.e.

On careful observation of the number line you will notice that the numbers that are greater in value are seen to be on the right side of the number line. I.e. if m
A set of real numbers can be depicted on the number line as mentioned earlier, by shading or coloring the points whose coordinates are elements of the sets.


I like to share this solve by the substitution method with you all through my article.

Example on Different Set of Real Numbers:

let us study different set of real numbers with examples.

The natural numbers, also called as counting numbers or positive integers, are the numbers 1,2,3,4 etc, achieved by adding 1 repeatedly. The set 1,2,3,4 of all natural numbers are represented by the symbol N.


The integer comprises of all the natural numbers, the negatives of the natural numbers, and zero. The set of all integers  I.e. {-3,-2,-1, 0, 1, 2, 3} are given by the symbol N.


The rational numbers are numbers that are in the form a/b, such that a and b are integers; b? 0. Since b may be equal to 1, every integer is a rational number. Other illustrations of rational numbers are 9/5, 4/5 and -34/3. The set of all rational numbers is represented by the symbol Q (keep in mind this is to show that rational numbers are quotients of integers). Rational numbers that are in decimal form either lapse or begin to replicate a similar pattern imprecisely.


Irrational number are decimal representation that is non- lapsing or non- replicating.  Examples are v3= 1.7320508, and p= 3.1415926.


The amalgamation of  different rational and irrational numbers is the set of Real Numbers.

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