Chain

A chain is a series of connected links which are typically made of metal. A chain may consist of two or more links.

Two distinct chains can be connected using a quick link which resembles a carabiner with a screw close rather than a latch.

Uses for chain

Uses for chain include:

Decoration

Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is transitive, antisymmetric, and total (this relation is denoted here by infix ≤). A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain.

If X is totally ordered under ≤, then the following statements hold for all a, b and c in X:

Antisymmetry eliminates uncertain cases when both a precedes b and b precedes a. A relation having the property of "totality" means that any pair of elements in the set of the relation are comparable under the relation. This also means that the set can be diagrammed as a line of elements, giving it the name linear.Totality also implies reflexivity, i.e., a ≤ a. Therefore, a total order is also a partial order. The partial order has a weaker form of the third condition. (It requires only reflexivity, not totality.) An extension of a given partial order to a total order is called a linear extension of that partial order.

Chain (unit)

A chain (ch) is a unit of length. It measures 66 feet, or 22 yards, or 100 links, or 4 rods (20.1168 m). There are 10 chains in a furlong, and 80 chains in one statute mile. An acre is the area of 10 square chains (that is, an area of one chain by one furlong). The chain has been used for several centuries in Britain and in some other countries influenced by British practice.

By extension, chainage (running distance) is the distance along a curved or straight survey line from a fixed commencing point, as given by an odometer.

Origin

The chain was commonly used with the mile to indicate land distances and in particular in surveying land for legal and commercial purposes. Starting in the 19th centary, the chain was used as a sub division with the mile to show distances between railway stations, tunnels and bridges. In medieval times, local measures were commonly used, and many units were adopted that gave manageable units; for example the distance from London to York could be quoted in inches, but the resulting huge number would be unmemorable. The locally used units were often inconsistent from place to place.