Talk:Collectively exhaustive events

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I changed the P(head) = 0.5, P(tail)=0.5, and P(head)+P(tail)=1 explanation because it gives the wrong impression of what collectively exhaustive means. For instance, say you're picking an integer, x, less than or equal to 10. P(x is even) = 0.5, P(x<6) = 0.5, so P(x is even)+P(x<6)=1 but the two events aren't collectively exhaustive because odd numbers greater than or equal to 6 are never chosen. In fact, P(x is even OR x<6) = 0.8.

I added the section about the comparison of mutual exclusivity with colletive exhaustion. I did the same thing with the wikipedia stub on mutually exclusive and crossed referenced both articles with each other. I am not a professional mathematician, so if I have made an error in this update please correct it and I'll have no worries.

capitalist

I removed the stub tag from this article because its scope is narrow enough to justify the short length. capitalist 03:39, 6 September 2005 (UTC)[reply]

Quotation from Couturat 1914:23

The following appears as a footnote on page 23

"As Mrs. LADD·FRANKLlN has truly remarked (BALDWIN, Dictionary of Philosophy and Psychology, article "Laws of Tbought"), 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)." (Louis Couturat, translated by Lydia Gillingham Robinson, 1914, The Algebra of Logic, The Open Court Publishing Company, Chicago and London.)

The above can be downloaded from googlebooks as a pdf. Am not sure what to do with this yet, except that the last paragraph looks quite wrong, especially from a historical perspective. The other place to look is Stephen Kleene 1952 Metamathematics. Or even way back into Boole etc in the ca 1850's. BillWvbailey (talk) 19:28, 1 September 2012 (UTC)[reply]

Removed History Section

I removed the history section because whoever wrote it was writing about the history of the term "mutually exclusive" when this Wiki entry is about "collectively exhaustive". For mutually exclusive events, go to that Wiki entry--we shouldn't be focusing on that concept in this entry. — Preceding unsigned comment added by 173.3.109.197 (talk) 16:06, 21 November 2012 (UTC)[reply]

Two of the quotes discuss "exhaustive" (of the universe of discourse, Ladd-Franklin) and only one of the three alternatives hold (Kleene). I pruned out the two quotes re mutual exclusion only and left in "collectively" exhaustive, i.e. both quotes are pertinent. BillWvbailey (talk) 16:48, 21 November 2012 (UTC)[reply]

I added italics to emphasize that the word "exhaustion" does in fact appear in the quotes (apparently anonymous didn't read the quotes very carefully). Also note that the article lead does in fact discuss "mutually exclusive"; the two ideas "mutual exclusion" and "exhaustion" are intimately connected. The adjective "collectively" is redundant. BillWvbailey (talk) 17:08, 21 November 2012 (UTC)[reply]

History insufficiently nearly exhaustive.

Jeremy Bentham used the term exhaustive in the set theory sense in his "Chrestomathia" of 1817, (available at http://archive.org/details/chrestomathiabe00bentgoog) and what is more he explained it in the following terms "words can, it is supposed, be necessary. To be exhaustive, the parts which, at each partition or division so made, are the results of the operation

— must, if put together again, be equal to the whole,

— and thus, and in this sense, exhaust (to use the word employed by logicians) the contents of the whole."

Accordingly it must already have been in use by that time in much the sense in which it is used here. Ngram also gives several books using the term in such senses in the 19th century. This was not in connection with statistics or probability, but the sense is so closely connected with set theory (in connection with which I was looking it up) that I am not sure why the two are separated. JonRichfield (talk) 14:30, 3 June 2013 (UTC)[reply]

Nice find. This would make a good addition to the article. As I recall, when I added the Ladd-Franklin and Kleene quotes I first hunted through my various googlebooks dating from the 19th C (starting around the time of Boole) but didn't find the words used anywhere. I'd expect (because of the classical "logicians", aka "the schoolmen" with their fussy syllogisms) that if there's anything earlier than the 18th C it would go all the way back to the ancient Greeks.

I agree with you that this logical priciple has much broader scope than statistics; e.g. the "switch" or "case" statements. Bill Wvbailey (talk) 21:58, 3 June 2013 (UTC)[reply]

Thanks Bill. Would you like to expand the content to at least mention such concepts, or create an article on partitioning and exhaustion? I'd prefer to keep it all together in this article, but the title seems to me to be too restrictive for that. If you would prefer that I did the legwork, I wouldn't mind, but then I'd like some helpful suggestions concerning what you would see as the right approach (say, splitting, uniting, renaming articles, redirs etc). Cheers, Jon JonRichfield (talk) 11:27, 5 June 2013 (UTC)[reply]

Anything you can do to improve this article would be appreciated by the community -- as it stands now this article is awful. When I added the quotes, I also added the four references. But none of them offer anything more a citation (i.e. origin) of the quotes. I've looked in my books and can find nothing -- in a book on information theory (in particular, conditional probability), in a book on machine learning (in particular "Bayesian Learning" and a formula that sums all the probabilities to 1), in a graduate-level engineering text on combinatorial and sequential "logic" (in particular, the generation of a Karnaugh map with its 2^n minterms and their combinations to "cover the map"), etc. Nothing at all about "collectively exhaustive events." I can't seem to locate in my library any statistics books worthy of the name. So my knowledge and library is not going to be of much use. Bill Wvbailey (talk) 14:23, 7 June 2013 (UTC)[reply]

Oh Blast! I'm not promising anything, but I'll have a look and see. I'll probably come back here before doing anything bold though! Cheers,

Jon JonRichfield (talk) 18:52, 8 June 2013 (UTC)[reply]