**Addition of Natural and Real Numbers**

To prove the usual properties of addition, one must first *define* addition for the context in question. Addition is first defined on the natural numbers. In set theory, addition is then extended to progressively larger sets that include the natural numbers: the integers, the rational numbers, and the real numbers. (In mathematics education, positive fractions are added before negative numbers are even considered; this is also the historical route)

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### Famous quotes containing the words numbers, real, addition and/or natural:

“Think of the earth as a living organism that is being attacked by billions of bacteria whose *numbers* double every forty years. Either the host dies, or the virus dies, or both die.”

—Gore Vidal (b. 1925)

“It is easier to discover a deficiency in individuals, in states, and in Providence, than to see their *real* import and value.”

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“The most important American *addition* to the World Experience was the simple surprising fact of America. We have helped prepare mankind for all its later surprises.”

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“The persons who constitute the *natural* aristocracy, are not found in the actual aristocracy, or, only on its edge; as the chemical energy of the spectrum is found to be greatest just outside of the spectrum.”

—Ralph Waldo Emerson (1803–1882)