# Q.e.d. Code

## Partial Order

### Sinopsis

A fully ordered set is one in which we can tell for any two members which one comes before the other. Think integers. A partially ordered set, however, only gives us an answer for some pairs of nodes. A directed acyclic graph defines a partial order over its nodes. Find out how to compute this partial order, and some of the ways in which it can be applied. The number of degrees of freedom in a system of equations is equal to the number of unknowns minus the number of equations. We can add unknowns, as long as we also add the same number of equations, without changing the behavior of the system. Then we can rewrite the equations, again without changing behavior, to solve for some of those unknowns in terms of others. Doing so, we divide the system into independent and dependent variables. The number of degrees of freedom is equal to the number of independent variables. In 1978, Leslie Lamport wrote "Time, Clocks, and the Ordering of Events in a Distributed System". In this paper, he constructs a clock that giv