A set is a group of entities categorized according to some conceptual constraints. It is a mental bracket enclosing certain entities whose simplified structure is abstracted from the complexities of chaotic nature. The member entities are recognised as conforming to a range of limitations. There are only conformists in a set. The entities of a set may be living things like the finches Carduelis carduelis or objects like bird-baths. They may be conceptual like numbers or perhaps... with care... even sets themselves.

Describing a unique group of entities in different ways doesn't create different sets. A set is determined by its members and not by how it is chosen to be described. A set described as... the set of all finches in the above image... and a set described as... the set of all feathered bipeds in the above image... are not different sets. They one set has been described in two different ways.

Expulsion from a set depends upon the flexibility of the rules of membership. Breaking a membership rule of a set described logically has rather harsh and immediate consequences. If a member of the set of integers has a fraction added to it, it is no longer an integer. Adding, subtracting or multiplying by a 'zero' goes unnoticed, but dividing by 'zero' is unforgivable. The moment an indiscretion is uncovered, the entry permit gets over-stamped with OUT. Breaking the membership rules of a social set may not be quite so instantaneous. If any of the group norms of clothing, language, food or whatever are transgressed, such deviance is often dealt with by an escalating range of controls. The deviant may firstly be persuaded to mend the error of their ways or to suffer punishment before the ultimate expulsion is actioned. One has to work quite hard at getting thrown out of the set consisting of all individuals with the same sex.

In order to avoid a number of academic dilemmas which have been promoted, it needs to be recognized that a set is an entity of a different degree of abstraction from the entity elements which form its contents. A finch is an entity which has a coherent spatio-temporal continuity conforming to concepts of finch-type structures and so we can contemplate the concept of a flock of finches. However... to state the obvious... although the flock of finches which we are now contemplating is itself a social structure of behavioural interactions... and as such could be thought of as an entity... it is not itself a finch. It cannot be included as a member of our set of finches. The set of finches cannot be a member of itself. Thus one contemplates a flock or charm of finches but not a flock of flocks, or a charm of charms; a herd of elephants but not a herd of herds. There is a team of players but a team of teams would be a different animal.

If it is deemed necessary to consider a set of sets... which some non-gardeners seem compelled to do... it must be recognized that those sets which form the members of the meta-set are of a different and lower level of abstraction. The properties which define a member set are not the same as the properties which define the set of sets. Thus a set can not sensibly be a member of itself because the members are a conceptual degree below that of the set itself.