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• Operations involving natural numbers
• Number theory

The natural numbers are the ordinary numbers, 1, 2, 3, etc., with which we count. They are sometimes called the counting numbers. They have been called natural because much of our experience from infancy deals with discrete (separate; individual; easily countable) objects such as fingers, balls, peanuts, etc. German mathematician Leopold Kronecker (1823–1891) is reported to have said, "God created the natural numbers; all the rest is the work of man."

Some disagreement exists as to whether zero should be considered a natural number. One normally does not start counting with zero. Yet zero does represent a counting concept: the absence of any objects in a set. To resolve this issue, some mathematicians define the natural numbers as the positive integers. An integer is a whole...