In mathematics, a locally finite poset is a partially ordered set P such that for all x, y ∈ P, the interval consists of finitely many elements.
Given a locally finite poset P we can define its incidence algebra. Elements of the incidence algebra are functions ƒ that assign to each interval of P a real number ƒ(x, y). These functions form an associative algebra with a product defined by
There is also a definition of incidence coalgebra.
In theoretical physics a locally finite poset is also called a causal set and has been used as a model for spacetime.
Famous quotes containing the words locally and/or finite:
“To see ourselves as others see us can be eye-opening. To see others as sharing a nature with ourselves is the merest decency. But it is from the far more difficult achievement of seeing ourselves amongst others, as a local example of the forms human life has locally taken, a case among cases, a world among worlds, that the largeness of mind, without which objectivity is self- congratulation and tolerance a sham, comes.”
—Clifford Geertz (b. 1926)
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)