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  2. Classification of discontinuities - Wikipedia

    en.wikipedia.org/wiki/Classification_of...

    The term removable discontinuity is sometimes broadened to include a removable singularity, in which the limits in both directions exist and are equal, while the function is undefined at the point . [a] This use is an abuse of terminology because continuity and discontinuity of a function are concepts defined only for points in the function's ...

  3. Discontinuities of monotone functions - Wikipedia

    en.wikipedia.org/wiki/Discontinuities_of...

    Then f is a non-decreasing function on [a, b], which is continuous except for jump discontinuities at x n for n ≥ 1. In the case of finitely many jump discontinuities, f is a step function. The examples above are generalised step functions; they are very special cases of what are called jump functions or saltus-functions. [8] [9]

  4. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    A function is continuous at a limit point p of and in its domain if and only if f(p) is the (or, in the general case, a) limit of f(x) as x tends to p. There is another type of limit of a function, namely the sequential limit. Let f : X → Y be a mapping from a topological space X into a Hausdorff space Y, p ∈ X a limit point of X and L ∈ Y.

  5. Oscillation (mathematics) - Wikipedia

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

    in a removable discontinuity, the distance that the value of the function is off by is the oscillation; in a jump discontinuity, the size of the jump is the oscillation (assuming that the value at the point lies between these limits from the two sides); in an essential discontinuity, oscillation measures the failure of a limit to exist.

  6. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to ...

  7. Trump aims to deport all immigrants in the US illegally - AOL

    www.aol.com/news/trump-says-aims-deport...

    By Ted Hesson. WASHINGTON (Reuters) -U.S. President-elect Donald Trump aims to deport all immigrants in the U.S. illegally over his four-year term but wants a deal to protect so-called "Dreamer ...

  8. Black Friday isn't over at Walmart: Here are the 10 best ...

    www.aol.com/lifestyle/black-friday-isnt-over-at...

    Walmart deals are always incredible this time of year, and while Walmart Black Friday deals haven't cooled down yet, they're only going to last a few more days. As Cyber Monday approaches, we took ...

  9. Monotonic function - Wikipedia

    en.wikipedia.org/wiki/Monotonic_function

    Monotonic function with a dense set of jump discontinuities ... is absolutely continuous; if is a monotonic function defined on an interval [,], then is ...