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  2. Fractional part - Wikipedia

    en.wikipedia.org/wiki/Fractional_part

    Graph of the fractional part of real numbers. The fractional part or decimal part [1] of a non‐negative real number is the excess beyond that number's integer part. The latter is defined as the largest integer not greater than x, called floor of x or ⌊ ⌋. Then, the fractional part can be formulated as a difference:

  3. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    The fractional part function has Fourier series expansion [19] {} = = ⁡ for x not an integer. At points of discontinuity, a Fourier series converges to a value that is the average of its limits on the left and the right, unlike the floor, ceiling and fractional part functions: for y fixed and x a multiple of y the Fourier series given ...

  4. Common logarithm - Wikipedia

    en.wikipedia.org/wiki/Common_logarithm

    Common logarithm. A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm is the logarithm with base 10. [ 1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well ...

  5. Periodic function - Wikipedia

    en.wikipedia.org/wiki/Periodic_function

    Periodic function. A periodic function also called a periodic waveform (or simply periodic wave ), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle. [ 1] For example, the trigonometric functions, which repeat at intervals of radians, are periodic functions ...

  6. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...

  7. Fractional coloring - Wikipedia

    en.wikipedia.org/wiki/Fractional_coloring

    Fractional coloring is a topic in a young branch of graph theory known as fractional graph theory. It is a generalization of ordinary graph coloring . In a traditional graph coloring, each vertex in a graph is assigned some color, and adjacent vertices — those connected by edges — must be assigned different colors.

  8. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    where () = [] denotes the fractional part of x and [] is the []-iterated function of the function . The proof is that the second through fourth conditions trivially imply that f is a linear function on [−1, 0].

  9. Refractive index - Wikipedia

    en.wikipedia.org/wiki/Refractive_index

    Refractive index. In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction ...

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