Where does cut collide?

A way of defining a real number as a division of all the rational numbers into two groups, a lower group and an upper group, where every number in the lower group is smaller than every number in the upper group. Dedekind's 1872 Stetigkeit und irrationale Zahlen (Continuity and Irrational Numbers) introduced this construction to give the real number line a rigorous foundation, so that a value with no rational name, such as the square root of two, is pinned down exactly by the split it makes among the rationals. The referent is a partition of an ordered number set that names one real number, not a transition between film shots, a division of a network, or a break in a DNA strand.[1]

Unit

One real number, given as a single split of the rationals into a lower and an upper part

Recovery means

Not applicable

Measured by

Constructed formally: a real number is identified with the pair of rational-number groups its split produces, and arithmetic is defined on those groups

A division of a network's nodes into two groups that separates a source from a sink, whose value is the total capacity of the links running from the source group to the sink group. Ford and Fulkerson's 1956 Maximal Flow Through a Network proved that the largest flow that can be pushed from source to sink equals the capacity of the smallest such division, the max-flow min-cut theorem. The referent is a set of network links whose removal severs source from sink, valued in units of capacity, not a split of the rationals, a film edit, or a break in a DNA strand.[2]

Unit

One partition of a network's nodes separating source from sink, valued by the capacity crossing it

Recovery means

Not applicable

Measured by

Found by maximum-flow algorithms, which locate the smallest cut capacity in a network of capacitated links