Infinity

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 a central concept. An integral, for example, is the sum of an "infinite number of infinitely small parts" — but still infinity is merely symbolic.

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