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3. In set theory and category theory, denotes the Cartesian product and the direct product. See also × in § Set theory. · 1. Denotes multiplication and is read as times; for example, 3 ⋅ 2. 2. In geometry and linear algebra, denotes the dot product. 3. Placeholder used for replacing an indeterminate element.
[57] [58] In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [59] [60] It is said to be an improper fraction, or sometimes top-heavy fraction, [61] if the absolute value of the fraction is greater than or ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
For example, 1 / 4 , 5 / 6 , and −101 / 100 are all irreducible fractions. On the other hand, 2 / 4 is reducible since it is equal in value to 1 / 2 , and the numerator of 1 / 2 is less than the numerator of 2 / 4 . A fraction that is reducible can be reduced by dividing both the numerator ...
def – define or definition. deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform.
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
This is not sharp; the gap between the functions is everywhere at least 1. Among the exponential functions of the form α x, setting α = e 2/e = 2.0870652... results in a sharp upper bound; the slightly smaller choice α = 2 fails to produce an upper bound, since then α 3 = 8 < 3 2. In applied fields the word "tight" is often used with the ...