Mathematics for Computer Science - ​Number Systems and Sets

​Number Systems and Sets 

1)
Natural Numbers 

Natural numbers are positive whole numbers. The number include 0.

The symbol of natural numbers  is used to represent the set of natural numbers such as ={0,1,2,3,4….}

A member of  that is added or multiplied with a member of  will result in a number which is also a member of .

The natural numbers are used in counting for instance “20 people in a bus” or to determine the order such as the “ 2nd person on the left side of the road”. 

As a result a natural numbers can be used as counters in computer programs.
2)
Integers 

Integers are different from natural numbers. Integers include a negative and positive whole numbers. The integer includes 0.

The symbol for the set of integers is . ={ -…4,-3,-2,-1,0,1,2,3,4…}  is known as ‘Zahlen’ in German for numbers.

A member of  if added or multiplied or deducted with another member of  also produce a member of 

As a result, integers are useful as counters in computer programs.

3)
Rational Numbers  

The symbols for a set of rational numbers is  which stands for quotient. Rational numbers are numbers that can be written in a fraction such as 3/4 or 2/9.

A rational number can be defined in the form of a/b where a and b are integers and b is not zero. A number such as 9 can also be written as 9/1 (rational number)  while a number -9 can also be written as -9/1 ( rational number). 
Therefore it can be concluded that  / set of rational numbers also include member of  / set of integers.

When a rational number is written in a decimal the number is either terminates after a finite number or digits such as 1/2 = 0.5 or recurs such as 1/3 = 0.33333…

4)
Irrational Numbers

There are numbers that cannot be written in the fraction forms. Examples include π, √2, or e.
The decimal numbers of irrational numbers are neither terminate or recur. For example, π
can be written as 3.1411592……… The series of digit will continue infinitely. 

Any computer representation of an irrational number will be a very close approximation.

5)
Real Numbers 

Real numbers are the set of all possible real world quantities. The symbol of set of real numbers is Real numbers are points of an infinitely long line. Real numbers are useful for measuring such as times taken to complete a run such as 12s, 19.9893s or 20.4s

 They include positive and negative numbers.  consists of all set of natural numbers , integers ,rational numbers and irrational numbers 

Info
An integer can be written in the form of fraction such as integer x as x/1.

The number is either rational or irrational.

All natural numbers are also integers

Test your knowledge on Number systems and set 

36
-36 is a natural number because it is a positive whole number with no decimal. 
-36 is also an integer because it is a again a positive whole number with no decimal.
-36 can be represented as 36/1 which is a fraction. A fraction can be associated with rational number. 
-36 also falls under real number due to the fact that it is a natural number, integer and rational number. 

90.5 
90.5 is a  number with a decimal form which is a finite number. It can be written as 181/2 as a fraction. It is not a natural number or integer .However  it is a rational number 
and also a real number 

3
3 is not a natural number or integer. It has a decimal answer which is not finite or terminated Therefore it is not a rational number. It is a irrational number. It also belongs to real number. 

16.50
16.50 is  a decimal number which is definite and terminated. 16.50 also can be written in the form of fraction as 33/2.

16.50 is not a natural number or integer. 
16.50 is a rational number and real number. 

8
8 is not a natural number or integer. 
8 has a decimal place. However it cannot be written in the form of fraction. The decimal version is neither finite or recurring. Therefore 8 is irrational number and real number.