On Counting Natural Numbers up to [ N = 1543 ]

by Frank C. Fung ( 1st published in October, 2012. )

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Section II - Defining the Categories for our Counting Purposes

Summary for the Section :

• In this Section , we shall define the Categories of { non-zero Natural Numbers } for our counting purposes .

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Recalling the Definition of Prime Numbers :

• Let us recall , at this very beginning , this definition of Prime Numbers :
  • IF :
    • any non-zero Natural Number [ P ] is a Prime Number ,

    THEN :

    • the only factors of [ P ] are :
      • [ 1 ] and the natural-number [ P ] itself .

• And we take special note here that :
  • [ 1 ] does qualify as a Prime Number under this definition ,

    and

  • [ 2 ] is the next natural number and it also qualifies as a Prime Number .

  The usual practice here in contemporary mathematics is to :

  • treat [ 1 ] as the Super-Prime ,
    • and put it into a category-by-itself ,

  • put [ 2 ] and all subsequent { Natural Numbers that qualify as Prime Numbers }
    • into a single-and-separate category , namely :
      • the Category of Prime Numbers .

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Defining the Categories :

• For our counting purposes , we shall stay in-line with the [ usual practice ] as delineated above .

  We shall therefore :

  • put [ 1 ] into the category [ Category Zero ] ,

  • put [ 2 ] and all the other Prime Numbers into [ Category I ] .

• Let us now also define the remaining categories of non-zero Natural Numbers
  • via this table below :

    Category	Description
    Category Zero	contains a single element - the natural number [ 1 ]
    Category I	contains all [ natural numbers ] that are [ prime numbers ]
    Category II	contains all [ natural numbers ] that are the product of 2 [ prime numbers ]
    Category III	contains all [ natural numbers ] that are the product of 3 [ prime numbers ]
    Category IV	contains all [ natural numbers ] that are the product of 4 [ prime numbers ]
    Category V	contains all [ natural numbers ] that are the product of 5 [ prime numbers ]
    Category VI	contains all [ natural numbers ] that are the product of 6 [ prime numbers ]
    Category VII	contains all [ natural numbers ] that are the product of 7 [ prime numbers ]
    Category VIII	contains all [ natural numbers ] that are the product of 8 [ prime numbers ]
    Category IX	contains all [ natural numbers ] that are the product of 9 [ prime numbers ]
    Category X	contains all [ natural numbers ] that are the product of 10 [ prime numbers ]
    Category XI	contains all [ natural numbers ] that are the product of 11 [ prime numbers ]
    and so-on-and-so-forth

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go to the next section : Section III - Explaining the Choice of [ N = 1543 ]

go to the last section : Section I - Introduction

return to the Counting Natural Numbers HomePage

Original dated 2012-10-08