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Natural numbers and integers

The natural numbers, or positive integers, are the numbers used for counting. They are the positive whole numbers.

$$1$$, $$2$$, $$3$$, $$\dots$$ are positive integers. $$3.2$$, $$1/4$$ and $$-1$$ are not integers.

$$\Tred{0}$$ is not a positive integer.

The integers are zero and the positive and negative whole numbers.

$$\dots$$, $$-2$$, $$-1$$, $$\Tred{0}$$, $$1$$, $$2$$, $$\dots$$ are integers. $$-1/3$$ and $$2.4$$ are not.

The symbol for the set of the integers is $$\mathbb{Z}$$.

The symbol for the set of the positive integers is $$\mathbb{Z}^+$$ or $$\mathbb{N}$$.

There are infinitely many positive integers and infinitely many integers.

This Babylonian clay tablet shows arithmetic using positive integers. Babylonians also used fractions and square roots, but no negative numbers or zero.
This Babylonian clay tablet shows arithmetic using positive integers. Babylonians also used fractions and square roots, but no negative numbers or zero.