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Collectively exhaustive events

In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 are collectively exhaustive, because they encompass the entire range of possible outcomes.

History
The term "exhaustive" has been used in the literature since at least 1914. Here are a few examples: The following appears as a footnote on page 23 of Couturat's text, The Algebra of Logic (1914): :"As Mrs. LADD·FRANKLlN has truly remarked (BALDWIN, Dictionary of Philosophy and Psychology, article "Laws of Thought"), the principle of contradiction is not sufficient to define contradictories; the principle of excluded middle must be added which equally deserves the name of principle of contradiction. This is why Mrs. LADD-FRANKLIN proposes to call them respectively the principle of exclusion and the principle of exhaustion, inasmuch as, according to the first, two contradictory terms are exclusive (the one of the other); and, according to the second, they are exhaustive (of the universe of discourse)." (italics added for emphasis) In Stephen Kleene's discussion of cardinal numbers, in Introduction to Metamathematics (1952), he uses the term "mutually exclusive" together with "exhaustive": :"Hence, for any two cardinals M and N, the three relationships M N are 'mutually exclusive', i.e. not more than one of them can hold. ¶ It does not appear till an advanced stage of the theory . . . whether they are '' 'exhaustive' '', i.e. whether at least one of the three must hold". (italics added for emphasis, Kleene 1952:11; original has double bars over the symbols M and N). ==See also==
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