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  2. Interval (mathematics) - Wikipedia

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

    Intervals are completely determined by their endpoints and whether each endpoint belong to the interval. This is a consequence of the least-upper-bound property of the real numbers. This characterization is used to specify intervals by mean of interval notation, which is described below.

  3. Unit interval - Wikipedia

    en.wikipedia.org/wiki/Unit_interval

    In mathematics, the unit interval is the closed interval [0,1], that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted I (capital letter I). In addition to its role in real analysis, the unit interval is used to study homotopy theory in the field of topology.

  4. Nested intervals - Wikipedia

    en.wikipedia.org/wiki/Nested_intervals

    4 members of a sequence of nested intervals. In mathematics, a sequence of nested intervals can be intuitively understood as an ordered collection of intervals on the real number line with natural numbers =,,, … as an index. In order for a sequence of intervals to be considered nested intervals, two conditions have to be met:

  5. Interval arithmetic - Wikipedia

    en.wikipedia.org/wiki/Interval_arithmetic

    Interval arithmetic (also known as interval mathematics; interval analysis or interval computation) is a mathematical technique used to mitigate rounding and measurement errors in mathematical computation by computing function bounds.

  6. Interval - Wikipedia

    en.wikipedia.org/wiki/Interval

    Interval (mathematics), a range of numbers Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets; A statistical level of measurement; Interval estimate; Interval (graph theory) Space-time interval, the distance between two points in 4-space

  7. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    A function is continuous on a semi-open or a closed interval; if the interval is contained in the domain of the function, the function is continuous at every interior point of the interval, and the value of the function at each endpoint that belongs to the interval is the limit of the values of the function when the variable tends to the ...

  8. Monotonic function - Wikipedia

    en.wikipedia.org/wiki/Monotonic_function

    In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ] [ 2 ] [ 3 ] This concept first arose in calculus , and was later generalized to the more abstract setting of order theory .

  9. Step function - Wikipedia

    en.wikipedia.org/wiki/Step_function

    In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. An example of step functions (the red graph).