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A cake with one quarter (one fourth) removed. The remaining three fourths are shown by dotted lines and labeled by the fraction 1 ⁄ 4. A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size ...
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]
Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero. In 830, Mahāvīra unsuccessfully tried to correct the mistake Brahmagupta made in his book Ganita Sara Samgraha : "A number remains unchanged when divided by zero."
An improper Riemann integral of the first kind, where the region in the plane implied by the integral is infinite in extent horizontally. The area of such a region, which the integral represents, may be finite (as here) or infinite. An improper Riemann integral of the second kind, where the implied region is infinite vertically.
As an example, when using an unsigned 8-bit fixed-point format (which has 4 integer bits and 4 fractional bits), the highest representable integer value is 15, and the highest representable mixed value is 15.9375 (0xF.F or 1111.1111 b). If the desired real world values are in the range [0,160], they must be scaled to fit within this fixed-point ...
If the problem mandates that the constraints be satisfied, as in the above discussion, the constraints are sometimes referred to as hard constraints.However, in some problems, called flexible constraint satisfaction problems, it is preferred but not required that certain constraints be satisfied; such non-mandatory constraints are known as soft constraints.
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