set

(noun)

a collection of distinct objects, considered as an object in its own right

Related Terms

  • recursion

Examples of set in the following topics:

  • Real Numbers, Functions, and Graphs

    • Functions relate a set of inputs to a set of outputs such that each input is related to exactly one output.
    • A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
    • Here, the domain is the entire set of real numbers and the function maps each real number to its square.
  • Parametric Equations

    • Parametric equations are a set of equations in which the coordinates (e.g., $x$ and $y$) are expressed in terms of a single third parameter.
    • For example, the simplest equation for a parabola $y=x^2$ can be parametrized by using a free parameter $t$, and setting $x=t$ and $y = t^2$.
    • Converting a set of parametric equations to a single equation involves eliminating the variable from the simultaneous equations.
  • Optimization

    • Mathematical optimization is the selection of a best element (with regard to some criteria) from some set of available alternatives.
    • Mathematical optimization is the selection of a best element (with regard to some criteria) from some set of available alternatives.
  • Average Value of a Function

    • An average is a measure of the "middle" or "typical" value of a data set.
    • In the most common case, the data set is a discrete set of numbers.
  • Inverse Functions

    • Instead of considering the inverses for individual inputs and outputs, one can think of the function as sending the whole set of inputs—the domain—to a set of outputs—the range.
    • Let $f$ be a function whose domain is the set $X$ and whose range is the set $Y$.
  • Sequences

    • Like a set, it contains members (also called elements, or terms).
    • Unlike a set, order matters in a sequence, and exactly the same elements can appear multiple times at different positions in the sequence.
    • Most precisely, a sequence can be defined as a function whose domain is a countable, totally ordered set, such as the natural numbers.
  • Approximate Integration

    • These methods rely on a "divide and conquer" strategy, whereby an integral on a relatively large set is broken down into integrals on smaller sets.
  • Applications of Multiple Integrals

    • As is the case with one variable, one can use the multiple integral to find the average of a function over a given set.
    • Given a set $D \subseteq R^n$ and an integrable function $f$ over $D$, the average value of $f$ over its domain is given by:
  • Further Transcendental Functions

    • Note that, for $ƒ_2$ in particular, if we set $c$ equal to $e$, the base of the natural logarithm, then we find that $e^x$ is a transcendental function.
    • Similarly, if we set $c$ equal to $e$ in ƒ5, then we find that $\ln(x)$, the natural logarithm, is a transcendental function.
  • Curve Sketching

    • The $x$-intercepts are found by setting $y$ equal to $0$ in the equation of the curve and solving for $x$.
    • Similarly, the y intercepts are found by setting $x$ equal to $0$ in the equation of the curve and solving for $y$.
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