Infinity or
is a symbol that represents a positive infinite quantity.
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 all close allBasic Examples (2)
Use as iterator limit:
Do arithmetic with infinite quantities:
Scope (7)
Use inf to enter :
Series expansion at :
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 Guides
Related Links
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0)
Text
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
BibTeX
@misc{reference.wolfram_2025_infinity, author="Wolfram Research", title="{Infinity}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Infinity.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_infinity, organization={Wolfram Research}, title={Infinity}, year={1996}, url={https://reference.wolfram.com/language/ref/Infinity.html}, note=[Accessed: 17-November-2025]}