# 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 .
• Certain arithmetic operations work with Infinity.
• NumberQ[Infinity] yields False.

# 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: