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On the most basic level, the natural numbers are the "counting numbers." For example:
$$1, 2, 3, 4, 5, 6...$$
The whole numbers are very similar but the number $0$ is added:
$$0, 1, 2, 3, 4, 5, 6...$$
The integers are the whole numbers with one important addition. The negative counterparts are included:
$$...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6...$$