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Zero represents a set with no elements.

The purpose of zero as a digit: In our decimal numbering system, in any number you use, for example 512, each of the digits has its own value, but it also has a value that depends on its position. For example, 5 is not simply 5, it is 5x100, because of the position where it appears. Often, a zero will be needed as a placeholder, to "push" other digits further to the left. For example, 107 is not the same as 17. The zero is required to put the 1 "into its rightful place".

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