Range

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that f can take as its argument varies over D, i.e.,

Note that among mathematicians, the word "image" is used more commonly than "range."

The range is a subset of Y and does not have to be all of Y.

Unfortunately, term "range" is often used to mean domain--its precise opposite--in probability theory, with Feller (1968, p. 200) and Evans et al. (2000, p. 5) calling the set of values that a variate X can assume (i.e., the set of values x that a probability density function P(x) is defined over) the "range", denoted by R_X (Evans et al. 2000, p. 5).

Even worse, statistics most commonly uses "range" to refer to the completely different statistical quantity as the difference between the largest and smallest order statistics. In this work, this form of range is referred to as "statistical range."

See also

Domain, Image, Line Segment Range, Map, Over, Statistical Range, Transformation Explore this topic in the MathWorld classroom

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References

Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, 2000.Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. New York: Wiley, 1968.

Referenced on Wolfram|Alpha

Range

Cite this as:

Weisstein, Eric W. "Range." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Range.html

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