is a symbol that represents a positive infinite quantity.
- can be entered as \[Infinity] or inf.
- In StandardForm, Infinity is printed as .
- Infinity is converted to DirectedInfinity.
- Certain arithmetic operations work with Infinity.
- NumberQ[Infinity] yields False.
Examplesopen allclose all
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:
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).
Wolfram Language. 1988. "Infinity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Infinity.html.
Wolfram Language. (1988). Infinity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Infinity.html