3/24/2024 0 Comments Math term range![]() ![]() So the verb usage is not specifically mathematical, and is omitted from math dictionaries the noun usage found in math dictionaries is also found in general dictionaries, but is specialized enough to single out in math dictionaries. In fact, if you look up "range" in, for example, Merriam-Webster (m-w.com), you find the technical definition of the noun as 7c, among other related uses within mathematics:ħ a : a sequence, series, or scale between limitsī : the limits of a series: the distance orĬ : the difference between the least and greatest values of an attribute or of theĨ a : the set of values a function may take onī : the class of admissible values of a variable Math definitions generally give only the specific technical sense of words your use of "range from this to that" is a common-language sense, which can be found in ordinary dictionaries, and doesn't need a special definition. I answered, starting with a definition from a standard American English dictionary: Thanks for writing to Dr. The anonymous student finds only this definition, as a noun, in math dictionaries why don’t they say what it means as a verb? And isn’t the fact that the values range from 72 to 94 more important than the mere difference? (If you think that’s wrong, we’ll get to that soon …) ![]() If the only definition of range is the difference, why do we say "They range."? We are always talking about "They range in age from, or they range in height, or they range in weight, or they range in size, etc.". ![]() I can find only one definition of range in the math dictionaries - the difference between the smallest and the largest number in a set. I’ll start with a question from 2003: Definitions of Range What is range? Mathematical and other usage Is “range” defined as the interval containing the data, or the difference between largest and smallest values, or 1 more than that? Yes! All three are used, and are useful. A recent question about two interpretations of the range of a data set in statistics leads us into some older questions and some mysteries. If the infimum does not exist, one says often that the corresponding endpoint is − ∞. The endpoints of an interval are its supremum, and its infimum, if they exist as real numbers. Definitions and terminology Īn interval is a subset of the real numbers that contains all real numbers lying between any two numbers of the subset. Notable generalizations are summarized in a section below possibly with links to separate articles. Unless explicitly otherwise specified, all intervals considered in this article are real intervals, that is, intervals of real numbers. The notation of integer intervals is considered in the special section below. Intervals are likewise defined on an arbitrary totally ordered set, such as integers or rational numbers. Interval arithmetic consists of computing with intervals instead of real numbers for providing a guaranteed enclosure of the result of a numerical computation, even in the presence of uncertainties of input data and rounding errors. For example, they occur implicitly in the epsilon-delta definition of continuity the intermediate value theorem asserts that the image of an interval by a continuous function is an interval integrals of real functions are defined over an interval etc. Intervals are ubiquitous in mathematical analysis. An interval can contain neither endpoint, either endpoint, or both endpoints.įor example, the set of real numbers consisting of 0, 1, and all numbers in between is an interval, denoted and called the unit interval the set of all positive real numbers is an interval, denoted (0, ∞) the set of all real numbers is an interval, denoted (−∞, ∞) and any single real number a is an interval, denoted. Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. In mathematics, a ( real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". All numbers greater than x and less than x + a fall within that open interval. For other uses, see Interval (disambiguation). For intervals in order theory, see Interval (order theory). This article is about intervals of real numbers and some generalizations. ![]()
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