# Order Dimension - Formal Definition

Formal Definition

The dimension of a poset P is the least integer t for which there exists a family

of linear extensions of P so that, for every x and y in P, x precedes y in P if and only if it precedes y in each of the linear extensions. That is,

### Other articles related to "formal definition":

Atomic SP-DEVS - Formal Definition
... The above controller for crosswalk lights can be modeled by an atomic SP-DEVS model ... Formally, an atomic SP-DEVS is a 7-tuple where is a finite set of input events is a finite set of output events is a finite set of states is the initial state is the time advanced function which defines the lifespan of a state where is the set of non-negative rational numbers plus infinity ...
Big O Notation - Example
... In typical usage, the formal definition of O notation is not used directly rather, the O notation for a function f(x) is derived by the following simplification ... One may confirm this calculation using the formal definition let f(x) = 6x4 − 2x3 + 5 and g(x) = x4 ... Applying the formal definition from above, the statement that f(x) = O(x4) is equivalent to its expansion, for some suitable choice of x0 and M and for all x > x0 ...

### Famous quotes containing the words definition and/or formal:

Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.
Willard Van Orman Quine (b. 1908)

Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?”
Horace Walpole (1717–1797)