# Single word for "division" into all possible cases for analysis

What is a good word for the act of "division into cases"?

This as in, for example, analyzing and enumerating all the possible cases and possibility of a situation, or in math proofs where one exhaust all possible values of a variable.

I can think of "categorize" or "classify". But I am not satisfied with them because them don't express the idea of identifying each individual possibility at the finest granularity.

Any suggestion is appreciated.

In case you aren't aware, this sort of proof is sometimes known as a Proof by Exhaustion.

My first suggestion adds little to your question, as you've used the word yourself, but I'd simply say dividing: The problem to be addressed is divided or sub-divided into cases. (See also break and break down.)

divide
divided; dividing transitive verb

• to separate into two or more parts, areas, or groups (e.g. divide the city into wards)
• to separate into classes, categories, or divisions (e.g. divide history into epochs)
• cleave, part (e.g. a ship dividing the waves)

from Merriam-Webster

If the cases fall into very natural divisions, then those cases may instead be enumerated:

enumerate
enumerated; enumerating transitive verb

• to ascertain the number of : count
• to specify one after another : list

from Merriam-Webster

Another nice alternative is the delineation of cases:

delineate

• Describe or portray (something) precisely.
• Indicate the exact position of (a border or boundary)

For something more "arty" you might say that the logical space is carved into distinct cases:

carve
carved; carving transitive verb

• to cut with care or precision (e.g. carved fretwork)
• to make or get by or as if by cutting —often used with out (e.g. carve out a career)
• to cut into pieces or slices (e.g. carved the turkey)

from Merriam-Webster

Some other potentially useful words, though I'm less convinced, are dissect, atomize and anatomize.

• Since my initial answer mostly used words that already appeared in the question, I've expanded it further. Commented Jun 14, 2017 at 15:04
• 'enumeration of cases' or 'proof by cases' is usually what it's called in practice. 'proof by exhaustion' might be the title of the wiki article but I rarely see that used anymore. Commented Jun 14, 2017 at 15:49
• Since my last comment, there has been some tidying, and the addition of a few further options, perhaps most notably the addition of break, as in "we break the problem into three cases". Commented Jun 15, 2017 at 7:43

you also can use: assort , categorize , pigeonhole , separate , sort

• This would be a better answer with some references.
– Davo
Commented Jun 14, 2017 at 14:21

The word quantized might fit, as it suggests that there is a definable minimum size.

From Merriam-Webster:

quantize

quantized; quantizing: transitive verb

1 : to subdivide (something, such as energy) into small but measurable increments

It sounds like you are talking about something that would be visually represented as a Tree Diagram (Tree Diagram Analysis) although it's not clear from your question whether you are doing something like a Fault Tree analysis using Boolean logic or perhaps closer to a Probability Tree or perhaps closer to a Decision Tree.

You could shorten this idea to tree analysis or even just tree as in I made a tree of the problem.

You could also use diagram as in I diagramed the problem or I made a diagram of the problem.

You could also use "flow* or flow analysis and in I flowed the problem or I made a flow analysis.

Similar to flow I think scheme or step-by-step might also work.

Consider elimination (reasoning by elimination).

freedictionary.org:

elimination
NOUN
[Wordnet 3.0]

3. analysis of a problem into alternative possibilities followed by the systematic rejection of unacceptable alternatives;
[syn: elimination, reasoning by elimination]