# Infinity

Infinity or

is a symbol that represents a positive infinite quantity.

# Examples

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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, https://reference.wolfram.com/language/ref/Infinity.html (updated 1996).

#### 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_2024_infinity, author="Wolfram Research", title="{Infinity}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Infinity.html}", note=[Accessed: 15-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_infinity, organization={Wolfram Research}, title={Infinity}, year={1996}, url={https://reference.wolfram.com/language/ref/Infinity.html}, note=[Accessed: 15-July-2024 ]}