Asymptotic in the context of "Point at infinity"

Early forms of perspectivism have been identified in the philosophies of Protagoras, Michel de Montaigne, and Gottfried Leibniz. However, its first major statement is considered to be Friedrich Nietzsche's development of the concept in the 19th century, influenced by Gustav Teichmüller's use of the term some years prior. For Nietzsche, perspectivism takes the form of a realist antimetaphysics while rejecting both the correspondence theory of truth and the notion that the truth-value of a belief always constitutes its ultimate worth-value. The perspectival conception of objectivity used by Nietzsche sees the deficiencies of each perspective as remediable by an asymptotic study of the differences between them. This stands in contrast to Platonic notions in which objective truth is seen to reside in a wholly non-perspectival domain.

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.

A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.

In group theory, an area of mathematics, an infinite group is a group whose underlying set contains infinitely many elements. In other words, it is a group of infinite order. The structure of infinite groups is often a question of mathematical analysis of the asymptotics of how various invariants grow relative to a generating set, or how a group acts on a topological or measure space. In contrast, the structure of finite groups is determined largely by methods of abstract algebra.