Every nonempty subset of the natural numbers has a least element in their usual order. Applying this principle to positive integer linear combinations proves Bézout's identity. This principle for the usual natural-number order is distinct from the general well-ordering theorem asserting that every set can be equipped with some well-order.
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Natural numbers are a set of positive integers that are commonly used for counting and ordering. The set of natural numbers typically includes: - The positive integers: 1, 2, 3, 4, 5, ... Some definitions include zero in the set of natural numbers, making it: - 0, 1, 2, 3, 4, 5, ...
