Infinity or

is a symbol that represents a positive infinite quantity.



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Basic 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:

Wolfram Research (1988), Infinity, Wolfram Language function, (updated 1996).


Wolfram Research (1988), Infinity, Wolfram Language function, (updated 1996).


@misc{reference.wolfram_2020_infinity, author="Wolfram Research", title="{Infinity}", year="1996", howpublished="\url{}", note=[Accessed: 15-April-2021 ]}


@online{reference.wolfram_2020_infinity, organization={Wolfram Research}, title={Infinity}, year={1996}, url={}, note=[Accessed: 15-April-2021 ]}


Wolfram Language. 1988. "Infinity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996.


Wolfram Language. (1988). Infinity. Wolfram Language & System Documentation Center. Retrieved from