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Some `O` is made up of `A` and `B`. Without reference to any further or external information `O{A, B}` is a definition one could tentatively provide.

`A` and `B` are themselves subject to definition, such as `A{a, b, c}`, `B{e, f, g}`. An expanded definition of `O` would be `O{ A(a, b, c), B(e, f, g) }`.

The array `A, B` consists of subsets of `O`; an `O` which is in this context a set. The strings `a, b, c` and `e, f, g` are elements of the sets `A` and `B` respectively.

To use familiar language, `O` is the parent set, `A, B` are the child sets, `a, b, c` and `e, f, g` are grandchild sets. The simple definition is an order of sets, so that:

```O
—A
—B
```

The expanded definition is an order of sets of sets, so that:

```O
—A
——a, b, c
—B
——e, f, g```

A definition must reflect such hierarchy. If one were to suggest that, say, `O{A, B, e}` they would effectively be arguing for an alteration in the order among the sets:

```O
—A
——a, b, c
—B
——f, g
—e```

In terms of structure the definitions `O{A, B}` and `O{ A(a, b, c), B(e, f, g) }` do complement one another. The latter analyses the former.

Whereas, the definitions in `O{A, B}` and `O{A, B, e}` cannot both be equally precise/valid, for their underlying order is different. They contradict one another.

Thus concludes this short syllogism on logically [in]valid definitions.