[[!redirects sequence]] #Contents# * table of contents {:toc} ## Definition ## A __net__ is a function $a: I \to A$ from a [[directed type]] $I$ to a type $A$. $I$ is called the __index type__, the terms of $I$ are called __indices__ (singular __index__), and $A$ is called the __indexed type__. A __sequence__ is a net whose index type is the [[natural numbers]] $\mathbb{N}$. ## Examples ## * The Cauchy approximations used to define the [[HoTT book real numbers]] are nets indexed by a dense subsemiring $R_{+}$ of the positive [[rational numbers]] $\mathbb{Q}_+$. ## See also ## * [[directed type]] * [[Cauchy structure]] * [[Cauchy net]]