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An increment is a small, unspecified, nonzero change in the value of a quantity. The symbol most commonly used is the uppercase Greek letter delta ( ). The concept is applied extensively in mathematical analysis and calculus.

Consider the case of the graph of a function y = f ( x ) in Cartesian (rectangular) coordinates, as shown in the figure. The slope of this curve at a specific point P is defined as the limit, as x approaches zero, of m = y / x , provided the function is continuous (the curve is not 'broken'). The value y / x depends on defining two points in the vicinity of P . In the illustration, one of the points is P itself, defined as ( x p , y p ), and the other is Q = ( x q , y q ), which is near P . The increments here are y = y q - y p and x = x q - x p . As point Q approaches point P , both of these increments approach zero, and the ratio of increments y / x approaches the slope of the curve at point P .

The term increment is occasionally used in physics and engineering to represent a small change in a parameter such as temperature, electric current, visible light intensity, or time.

Also see Mathematical Symbols .

This was last updated in September 2005
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