The limit concept is essential to understanding the real number system and its distinguishing characteristics. In one sense real numbers can be defined as the numbers that are the limits of convergent sequences of rational numbers. One application of the concept of limits is on the derivative. The derivative is a rate of flow or change, and can be computed based on some limits concepts. Limits are also key to calculating intergrals (expressions of areas). The integral calculates the entire area of a region by summing up an infinite number of small pieces of it. Limits are also part of the iterative process. An iteration is repeatedly performing a routine, using the output of one step as the input of the next step. Each output is an iterate. Some successful iterates can get as close as desired to a theoretically exact value.
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