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2. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ⁠ ⁠, where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include ⁠ 1 2 ⁠, − ⁠ 8 5 ⁠, ⁠ −8 5 ⁠, and ⁠ 8 −5 ⁠.

3. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [ 1]

4. Harmonic series (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Harmonic_series_(mathematics)

   Therefore, the result is a fraction with an odd numerator and an even denominator, which cannot be an integer. [17] More strongly, any sequence of consecutive integers has a unique member divisible by a greater power of two than all the other sequence members, from which it follows by the same argument that no two harmonic numbers differ by an ...

5. 3D rotation group - Wikipedia

   en.wikipedia.org/wiki/3D_rotation_group

   The group of all 3 × 3 orthogonal matrices is denoted O(3), and consists of all proper and improper rotations. In addition to preserving length, proper rotations must also preserve orientation. A matrix will preserve or reverse orientation according to whether the determinant of the matrix is positive or negative.

6. Euler–Maclaurin formula - Wikipedia

   en.wikipedia.org/wiki/Euler–Maclaurin_formula

   The Euler–Maclaurin formula provides expressions for the difference between the sum and the integral in terms of the higher derivatives f(k)(x) evaluated at the endpoints of the interval, that is to say x = m and x = n . Explicitly, for p a positive integer and a function f(x) that is p times continuously differentiable on the interval [m,n ...

7. Number Forms - Wikipedia

   en.wikipedia.org/wiki/Number_Forms

   Number Forms is a Unicode block containing Unicode compatibility characters that have specific meaning as numbers, but are constructed from other characters. They consist primarily of vulgar fractions and Roman numerals. In addition to the characters in the Number Forms block, three fractions (¼, ½, and ¾) were inherited from ISO-8859-1 ...