## Natural 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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## Comments

Do imaginary numbers belong on this page?

No. Imaginary numbers are not real.

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.

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

0 and {1, 2, 3, …} = {0, 1, 2, 3, …}

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ah, and = plus.

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

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.