The Chained Sets
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The Chained Sets

Given a set A of two o more elements, in which all its elements A (a1, a2, a3, a4, a5, ... an) are linked one after the other in the form of a chain, (row, sequence, series, etc.) by means of a common nexus --p-- which consisting of any property, rule, even by the simple physical union of its elements, A (a1--p--a2--p--a3--p--a4--p--a5.......--p--an).
Such that every element n belonging to set A (nEA), is joined to the next one n+1, if there is, following this common union nexus or condition --p--.
n E A
n--p--n+1

The first element of the chain n = 1 will be the one that begins to apply the union nexus, when this quality can define the chain.
For example
A row of people waiting for the train. Nexus: waiting for the train in an orderly way.
Algorithm series for Pi. Nexus: algorithmic formula.

* Note,. the connecting nexus --p--, can be replaced by a simple sign - or another convention sign (a1-- a2 -- a3 -- a4 --.....-- an) in the general representation, and to the appropriate one in each particular set, for example in the sum A (3 + 2 + 6 + 8)

Then, chained set is a set in which each of its elements is joined to the following one in row, series or succession in chain way by means of any type of union, including the simple physical union of the elements.
For example, the links of a chain; the natural numbers ordered in succession; a row of people; series of powers, etc.
The main components are two:
1.- The elements of the chained set
2.- The union nexus that can be rules, properties, etc. or simple physical union of the elements.
In this way chained means that all its elements are linked together, one after another, by mean of some property, characteristics, purpose or ordering rule.
Another main property is that since it is a chain of elements, if the chain is broken by eliminating one of the links, this chain or set is divided into two chained sets.
Then the chained set is a special form of elements set with its own ordering and characteristics.

Thank you firends.