Definition:Natural Numbers/Historical Note

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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.