Natural and Whole Numbers

NumbersNatural numbers are counting numbers.

Counting starts from 1 and goes forward for ever.

But counting refers to things.

Counting deals with half of the dichotomy, “Nothing-Something”

To represent the dichotomy, the number zero for NOTHING must be added to the set of natural numbers.

So, the set of numbers defined as,

0 and {1, 2, 3, …}

is the set of WHOLE NUMBERS.


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  • Chris Thompson  On February 9, 2014 at 9:11 PM

    Do imaginary numbers belong on this page?

  • vinaire  On February 9, 2014 at 9:13 PM

    But zero is unique. It is not like the counting numbers.

    Zero adds an abstract aspect to the numbers.

    Zero cannot be defined quantitatively.

    Qualitatively, zero may be used as a reference point.

    But, zero can have any number of qualities.


  • Chris Thompson  On February 9, 2014 at 9:14 PM

    Why is 0 not placed inside the brackets of the set of whole numbers?

  • MarkNR  On February 9, 2014 at 11:51 PM

    The philosophy of mathematics can get a bit circular, (empty set) but the principals of arithmetic are invaluable to logical thinking.

    • vinaire  On February 10, 2014 at 5:53 AM

      A SET is a collection of items. When there is no item in a set then it would be an empty set.

      But when a set contains 0 as a number, 0 is looked upon as an item. A set containing 0 is not an empty set.

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