How to Identify Numbers, that are Members of the Different Sets of Numbers

Every Number is a Member of a Set of Numbers. Some Numbers are Members of at most Two Sets, and some Numbers are Members of every Set. This Article will help to Identify to what Sets of Numbers, a Number is a Member of, when the Number is called upon.

Difficulty: Easy

Instructions

Things You'll Need:

• Paper
• Graph Paper
• Pencil

1. There are many SETS of Numbers. The SETS of Numbers we will be working with, are: THE SET of NATURAL NUMBERS, THE SET of WHOLE NUMBERS, THE SET of INTEGERS, THE SET of RATIONAL NUMBERS, THE SET of IRRATIONAL NUMBERS, THE SET of REAL NUMBERS, THE SET of IMAGINARY NUMBERS and THE SET of COMPLEX NUMBERS. (A COMPLEX NUMBER is a Number that is the Sum or Difference of a REAL NUMBER with an IMAGINARY NUMBER).

2. The following letters will be used for the following set of numbers.
   N= The Set of Natural Numbers.
   W= The Set of Whole Numbers.
   Z= The Set of Integers.
   Q= The Set of Rational Numbers.
   Ir= The Set of Irrational Numbers.
   R= The Set of Real Numbers.
   Im= The Set of Imaginary Numbers.
   C= The Set of Complex Numbers.
   In the Images that follow, the sets to which the numbers belong will be written above the graph of that number.

3. 
    

   An Answer to the Question, " To what Set of Numbers is the Number TWO ( 2 ) a Member of? ". An Answer would be,... " The Number ( 2 ) is a Member of ALL the SETS of Numbers, mentioned in Step #1, except for the SET of Irrational Numbers and the Set of Imaginary Numbers. Please Click on the Image on the Left to see the Graph of ( 2 ) on the Number Line.

4. 
    

   The Number Negative Two ( -2 ), is a Member of the following Sets of Numbers: The Set of Integers, The Set of Rational Numbers, The Set of Real Numbers and the Set of Complex Numbers. Please click on the Image to the Left to see the graph of ( -2 ) on the Number Line.

5. 
    

   The Number ( 1/2 ), is a Member of The following Sets of Numbers: The Set of Rational Numbers, The Set of Real Numbers and the Set of Complex Numbers. Please click on the Image on the Left to see the Graph of ( 1/2 ) on the Number Line.

6. 
    

   The Number, The Square Root of ( 2 ), is a Member of the following Sets of Numbers: The Set of Irrational Numbers, the Set of Real Numbers and the Set of Complex Numbers. Please click on the Image to the Left to see the Graph of The Square Root of ( 2 ).

7. The Number, The Square Root of ( -4 ), is ( 2i ), where ( i ) is Defined as The Square Root of ( -1 ). So the Square Root of ( -4 ) can be expressed as the Product of,... The Square Root of ( 4 ) and The Square Root of ( -1 ), which is the Product of ( 2 ) and ( i ) that is
   ( 2i ). By definition ( 2i ) is an Imaginary Number,

8. 
    

   The Number, ( 2i ), is a Member of the following Sets of Numbers, The Set of Imaginary Numbers and The Set of Complex Numbers. Please click on the Image to the Left to see the Graph of ( 2i ). ( NOTE: ( 0 + 2i) is a Complex Number, and ( 0 + 2i ) = ( 2i )).

9. 
    

   The Number, ( 2 + 2i ), is a Complex Number. So ( 2 + 2i ) is a Member of The Set of Complex Numbers. Please click on the Image to the Left to see the Graph of ( 2 + 2i ).

Tips & Warnings

• Any number you choose will be similar to the example we gave above. So, one can easily identify a number in relationship to what set of numbers it belongs.
• Note: This article is about those numbers that belong to the basic sets of numbers.