# Infinity

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**Infinity**, usually represented by the symbol \(∞\), is a mathematical concept that indicates a "number" larger than any other number. It has different meanings across different branches in mathematics.

To googologists, infinity is a meaningless cop-out from the race to invent large finite numbers. However, some mathematical objects that could be called "infinities" are useful to googologists. Ordinal infinities (transfinites) are vitally important in measuring the growth rates of functions, in particular the fast-growing hierarchy.

In traditional algebra, infinity is meaningful only as a symbol, not a number that can be legitimately manipulated. One use is the definition of open intervals such as \([5,\infty)\), or inequalities like \(n < \infty\). In differential and integral calculus, however, infinity is one of central concepts. An integral, for example, is the sum of an "infinite number of infinitely small parts" — but still infinity is merely symbolic.

In complex analysis, the Riemann sphere is defined as \(\mathbb{C} \cup \{\infty\}\), where \(\infty\) is an unsigned infinity.

The term "Infinity Scraper", defined by Jonathan Bowers, refers to any number larger than tridecal. The term is, of course, hyperbolic.

Related to the "regular" mathmatical concept of infinity is complex infinity, defined as an infinite quantity which has an undefined complex argument.^{[1]}

A super task is a task that has an infinite amount of steps but it can be completed in a finite length of time.