Groups Are Not Unique

While an individual object in a group may have a unique identity, the group itself is only identifiable by its boundaries. In most cases groups are dynamic over time, changing in membership and expanse. Groups can be almost infinite or reduced to zero. In computing, arrays, lists, and file folders can be thought of as group containers. While the containers can be named using UniqueIdentifiers, the group itself is not unique.

Theories on group representation"

Mathematical Representations of groups - http://en.wikipedia.org/wiki/Category:Representation_theory_of_groups
Computer Representation of g.Groups - http://en.wikipedia.org/wiki/Class_%28computer_science%29

Are you sure, that this link is appropriate? It is about MathematicalGroup?s, which have little in common with collections/sets.

Not being a mathematician, I will not argue about common relationships, but to me, much of ProgrammingIsMath. In programming we continually are involved with principles which have their roots in Mathematical Relationships:

Points (location)
Lines (direction)
Planes, surfaces and edges (area)
Spaces (volume)
Angles (between lines or bearings)
Calculation (processes, formulas and relationships)
Integration (processes, formulas and relationships)
Differentiation (processes, formulas and relationships)
Solutions (complex relationships)
Theorems (statements to prove)
Postulations (derived from theorems)
Proofs (testing, reliability, trustworthiness. )
Sets (groupings)
Series (groupings)
Classes (grouping and relationships)
Physical constants (many derived from series)
Sums and Averages (another form used often of calculations)
Etc.

If programming is math, it ought to be precise, and not make simple errors like confusing the mathematical concept of a "group" (consult any text on abstract algebra), with a "group" as a generic English term for a collection. Perhaps this page should be renamed CollectionsAreNotUnique?, to avoid this particlar (unfortunate) use of the term "group", which is (almost) never used to refer to a collection in ComputerScience jargon?

CategoryOrganization