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  2. Interval (mathematics) - Wikipedia

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

    All numbers greater than x and less than x + a fall within that open interval. In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. A real interval can contain ...

  3. Extended real number line - Wikipedia

    en.wikipedia.org/wiki/Extended_real_number_line

    On the other hand, the function / cannot be continuously extended, because the function approaches as approaches 0 from below, and + as approaches 0 from above, i.e., the function not converging to the same value as its independent variable approaching to the same domain element from both the positive and negative value sides.

  4. Function space - Wikipedia

    en.wikipedia.org/wiki/Function_space

    The factorial notation X! may be used for permutations of a single set X. In functional analysis, the same is seen for continuous linear transformations, including topologies on the vector spaces in the above, and many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and Banach spaces.

  5. Limit of a function - Wikipedia

    en.wikipedia.org/wiki/Limit_of_a_function

    This generalization includes as special cases limits on an interval, as well as left-handed limits of real-valued functions (e.g., by taking T to be an open interval of the form (–∞, a)), and right-handed limits (e.g., by taking T to be an open interval of the form (a, ∞)).

  6. Uniform continuity - Wikipedia

    en.wikipedia.org/wiki/Uniform_continuity

    The difference between uniform continuity and (ordinary) continuity is that, in uniform continuity there is a globally applicable (the size of a function domain interval over which function value differences are less than ) that depends on only , while in (ordinary) continuity there is a locally applicable that depends on both and . So uniform ...

  7. Compact space - Wikipedia

    en.wikipedia.org/wiki/Compact_space

    Per the compactness criteria for Euclidean space as stated in the Heine–Borel theorem, the interval A = (−∞, −2] is not compact because it is not bounded. The interval C = (2, 4) is not compact because it is not closed (but bounded). The interval B = [0, 1] is compact because it is both closed and bounded.

  8. Unit interval - Wikipedia

    en.wikipedia.org/wiki/Unit_interval

    In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology. In the literature, the term "unit interval" is sometimes applied to the other shapes that an interval from 0 to 1 could take: (0,1], [0,1), and (0,1). However, the notation I is most commonly reserved for the closed interval [0,1].

  9. Infinite-dimensional vector function - Wikipedia

    en.wikipedia.org/wiki/Infinite-dimensional...

    If [,] is another interval in its domain then the two chords are said to be non−overlapping chords if [,] and [,] have at most one end−point in common. [1] Intuitively, two non−overlapping chords of a curve valued in an inner product space are orthogonal vectors if the curve makes a right angle turn somewhere along its path between its ...