# Translations of Encyclopedia about Mathematics

## Natural and Whole Numbers

The most simple numbers are natural numbers, which we use to count the simple number of objects. Natural numbers are positive and start with 1, 2, 3, 4, 5, …

This set of numbers includes all positive numbers of any size and is essentially infinite in number. Three dots ("…") also means "etc.".

Natural numbers are described mathematically as:

N = { 1,2,3,4,5,6,…}

Today, the number zero is often included as a natural number, in which, mathematically, it would be written as:

N0 = { 0,1,2,3,…}

With each (positive) natural number from the N set, there exists a negative number (for example, -1 for 1, -2 for 2 and so on). We call these numbers negative numbers.

Whole numbers are made of natural numbers and negative numbers, including the number zero.

The set of whole numbers are expressed as:

Z = { …,-2,-1,0,1,2,3,…}

Or, we can express the subset of only positive whole numbers as:

Z+ = { 1,2,3,4,5,6…}

Or the subset of only negative whole numbers as:

Z- = { -1,-2,-3,-4,-5,…}

In India, negative numbers already existed around the year 700. The Greeks then tried to introduce it around the year 250 and its practical use was used when calculating property and debts. In Europe, the turning point for so-called Arithmetic Integers was instigated by Michael Stifel in the year 1544. However, it was only until the 19th century did whole numbers become permanently entrenched in mathematics, thanks to Hermann Hankel.

Whole numbers include natural numbers and it can be said that Z is a superset of N and that N is a subset of Z.

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