# Definition:Natural Numbers/Historical Note

## Historical Note on Natural Numbers

The **natural numbers** were the first numbers to be considered.

Their earliest use was in the sense of ordinal numbers, when they were used for counting.

The origin of the name **natural numbers** (considered by some authors to be a misnomer) originates with the Ancient Greeks, for whom the only numbers were the strictly positive integers $1, 2, 3, \ldots$

It is customary at this stage to quote the famous epigram of Leopold Kronecker, translated from the German in various styles, for example:

*God created the natural numbers, and all the rest is the work of man.*

The exact word he used was **Zahlen**, which some translate as **integers**; the distinction is of little importance in this context.

The intuitionist viewpoint has that the **natural numbers** can be accepted as a primitive concept, despite the fact that they are infinite in number.

## Sources

- 1939: E.G. Phillips:
*A Course of Analysis*(2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Number: $1.1$ Introduction - 1980: David M. Burton:
*Elementary Number Theory*(revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.1$ Mathematical Induction - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**intuitionism** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**intuitionism**