Infinity
Infinity or 
is a symbol that represents a positive infinite quantity.
Details
can be entered as \[Infinity] or 
inf
. - In StandardForm, Infinity is printed as
. - Infinity is converted to DirectedInfinity[1].
- Certain arithmetic operations work with Infinity.
- NumberQ[Infinity] yields False.
Examples
open allclose allScope (7)
to enter 
Infinite limits of integration and summation:
Extended arithmetic with infinite quantities:
In this case the result depends on the growth rates of the two terms:
Use infinite quantities in predicates:
Find values of mathematical functions at infinities:
For some functions there is no definite limit, but a limiting interval:
In this case no limiting interval exists:
Mathematical functions can also return infinite quantities at finite points:
Cases finds matches only at the first level by default:
Set the level to Infinity to include all levels:
Applications (2)
Stirling's asymptotic approximation:
Setting the precision to Infinity will produce a rational approximation:
Some functions require infinite precision or exact input:
Apply SetPrecision to the whole expression to rationalize all inexact numbers:
Neat Examples (1)
Use an infinite WorkingPrecision in Plot:
Related Links
The Wolfram Functions SiteText
Wolfram Research (1988), Infinity, Wolfram Language function, https://reference.wolfram.com/language/ref/Infinity.html (updated 1996).
CMS
Wolfram Language. 1988. "Infinity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Infinity.html.
APA
Wolfram Language. (1988). Infinity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Infinity.html