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👉 Positive real numbers in the context of Interval (mathematics)

In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. A real interval can contain neither endpoint, either endpoint, or both endpoints, excluding any endpoint which is infinite.

For example, the set of real numbers consisting of $0$ , $1$ , and all numbers in between is an interval, denoted $[0, 1]$ and called the unit interval; the set of all positive real numbers is an interval, denoted $(0, \infty)$ ; the set of all real numbers is an interval, denoted $(-\infty, \infty)$ ; and any single real number $a$ is an interval, denoted $[a, a]$ .

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Positive real numbers in the context of Geometric mean

In mathematics, the geometric mean (also known as the mean proportional) is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of ⁠ $n$ ⁠ numbers is the $n$ th root of their product, i.e., for a collection of numbers $a 1, a 2, ..., a n$ , the geometric mean is defined as

When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm ⁠ $\ln$ ⁠ of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function ⁠ $\exp$ ⁠,

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Positive real numbers in the context of "Interval (mathematics)"

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👉 Positive real numbers in the context of Interval (mathematics)

Positive real numbers in the context of Geometric mean