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,

Read more about this topic:  Order Dimension

Famous quotes containing the words formal and/or definition:

    The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce formal instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.
    David Elkind (20th century)

    The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.
    Jean Baudrillard (b. 1929)