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*), and the other is

_{p}*Q*= (

*x*,

_{q}*y*), which is near

_{q}*P*. The increments here are

*y*=

*y*-

_{q}*y*and

_{p}*x*=

*x*-

_{q}*x*. As point

_{p}*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

*Posted by:*Margaret Rouse

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