infinity

(noun)

a number that has an infinite numerical value that cannot be counted

Related Terms

  • error

Examples of infinity in the following topics:

  • Infinite Limits

    • Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
    • Limits involving infinity can be formally defined using a slight variation of the $(\varepsilon, \delta)$-definition.
    • If the degree of $p$ is greater than the degree of $q$, then the limit is positive or negative infinity depending on the signs of the leading coefficients;
    • If the limit at infinity exists, it represents a horizontal asymptote at $y = L$.
    • Therefore, the limit of this function at infinity exists.
  • Precise Definition of a Limit

    • Therefore, the limit of this function at infinity exists.
    • Therefore, the limit of this function at infinity exists.
  • Finding Limits Algebraically

    • The limit of $f(x)= \frac{-1}{(x+4)} + 4$ as $x$ goes to infinity can be segmented down into two parts: the limit of $\frac{−1}{(x+4)}$ and the limit of $4$.
    • Therefore, the limit of $f(x)$ as $x$ goes to infinity is $4$.
  • Cylinders and Quadric Surfaces

    • A cylinder can be seen as a polyhedral limiting case of an $n$-gonal prism where $n$ approaches infinity.
  • Curve Sketching

    • Similarly, removing all but the terms of highest order from the equation and solving gives the points where the curve meets the line at infinity.
  • Indeterminate Forms and L'Hôpital's Rule

    • That limit could converge to any number, or diverge to infinity, or might not exist, depending on what the functions $f$ and $g$ are.
  • Sequences

    • The infinity symbol, $\infty$, is often used as the superscript to represent the sequence that includes all integer $k$-values starting with a certain one.
  • Improper Integrals

    • Such an integral is often written symbolically just like a standard definite integral, perhaps with infinity as a limit of integration.
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