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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.

5 Answers 5

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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)

from Oxford Living Dictionaries

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.

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  • 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.
    – Mitch
    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
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you also can use: assort , categorize , pigeonhole , separate , sort

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

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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.

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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]

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