Talk:countable set

uncountable set
An uncountable set is a set that's uncountable, nothing more and nothing less. —Mr. Granger (talk • contribs) 03:01, 10 January 2014 (UTC)
 * Delete. --WikiTiki89 03:04, 10 January 2014 (UTC)
 * Keep per Talk:free variable reasoning. The sense of "countable" or "uncountable" applied here is specific to sets. Keep also prime number, free software and other similarly formed items. --Dan Polansky (talk) 21:47, 10 January 2014 (UTC)
 * I don't understand your reasoning. The term manic-depressive is specific to people, but that doesn't mean we should have an entry for manic-depressive person. "Free variable" and "prime number" may be set phrases in some way, but "uncountable set" simply isn't. —Mr. Granger (talk • contribs) 22:14, 10 January 2014 (UTC)
 * The term "uncountable" is not specific to sets; it is the specific meaning of "uncountable" that is specific to sets. I think the most natural entry for the notion is "uncountable set", not "uncountable". Likewise, I find "open set" a better location for a notion than "open". Similarly for rational number (rational, sense 4: "Of a number, capable of being expressed as the ratio of two integers") and other items listed at Talk:free variable. I do not think I am making an argument strictly in terms of CFI, but CFI does not know "set phrase" mentioned by you as a criterion either, a criterion that was being mentioned in RFD as early as back in 2007. --Dan Polansky (talk) 22:46, 10 January 2014 (UTC)
 * Sense 5 of single is specific to people - does that mean we should have an entry for single person? —Mr. Granger (talk • contribs) 22:56, 10 January 2014 (UTC)
 * That's a good question. I would probably be okay with our having single person, but I do not find this as compelling as "free variable" and other technical terms that I learn and store in the mind as a pair " ". --Dan Polansky (talk) 23:15, 10 January 2014 (UTC)


 * Keep The term derives from a specific meaning in the field of mathematics that is not obvious to the average layperson. For me especially, I remember hearing the term 'countable' evoking the image of "being able to count with both hands, on one's fingers" but not realizing until later it refers to an infinite set with a one-to-one mapping. The same goes for the entry below. TeleComNasSprVen (talk) 02:48, 11 January 2014 (UTC)
 * That definition is at countable - what does that have to do with keeping these entries? —Mr. Granger (talk • contribs) 02:51, 11 January 2014 (UTC)
 * Keep. The deletionism on the English Wiktionary is beyond my understanding. You cannot count uncountable nouns while you can count uncountable sets; their elements are uncountable (i.e. there are more elements than integers). — T AKASUGI Shinji (talk) 10:21, 11 January 2014 (UTC)
 * Keep. I agree that deletionism on Wiktionary is going crazy once again. It's very discouraging to add technical, scientific, linguistic, medical or computer terms because they can be flagged as SOP. Even quoting respectable dictionaries don't seem to have any influence. In science, uncountable set and countable set are distinct terms and any dictionary should be proud to have them because it provides information on mathematical terms. We may keep north pole, gas station, blood type or other everyday term, everybody is familiar with and don't feel comfortable RFD-ing but if it's a bit longer and used more narrowly, then a term gets under threat. Let's say a computer term "materialized view", which is completely different from a normal database view. Judging by the logic of new active deletionists, there is no point in creating such terms, so we have to let people wanting to know such terms use other dictionaries, go somewhere else. We have to review our CFI. I know that even mentioning some common terms, such as north pole, gas station, blood type can cause more deletions but we have to do something about this madness, it should stop.--Anatoli (обсудить/вклад) 00:14, 13 January 2014 (UTC)
 * As someone who has studied a lot of set theory, I am actually very familiar with uncountable and countable sets. In a mathematical context, putting "(un)countable" and "set" together does not change the meaning of either word and does not add any unexpected new meaning. --WikiTiki89 00:20, 13 January 2014 (UTC)
 * A myriad of other terms don't add any unexpected new meaning, like "lung cancer" but they should be kept as specific terms. --Anatoli (обсудить/вклад) 00:36, 13 January 2014 (UTC)
 * I'm not a cancer expert, but I'm sure there are specific things about lung cancer that cannot be deduced simply from lung and cancer. With uncountable set, that's not the case. Not to mention that it's not even a set term: there are (un)countable sets, (un)countable fields, (un)countable groups, (un)countable rings, etc. --WikiTiki89 00:51, 13 January 2014 (UTC)
 * There is a huge number of technical, linguistic, medical and cultural term, which can be decomposed into parts and deduced without any change in meanings like comparative case, present tense, mammary gland, assembly language, film director. They are still kept (even if there is no RFD discussion, film director was kept because of 映画監督). --Anatoli (обсудить/вклад) 01:14, 14 January 2014 (UTC)
 * Except that "(un)countable set" is not a technical term in mathematics; "countable" and "uncountable" are technical terms and these terms can be applied to sets, fields, groups, rings, etc. Do you think we should have countable field, uncountable field, countable group, uncountable group, countable ring, uncountable ring, etc.? None of these benefit anyone, it is sufficient to know countable/uncountable and set, field, group, ring, etc. --WikiTiki89 01:26, 14 January 2014 (UTC)
 * A common collocation becomes a term if it's used often enough and is of interest to many people. Wikipedia articles and dictionary articles confirm that uncountable set and countable set are such terms. E.g., a "habitable zone" is a free form collocation but it may become a term, if it hasn't already, since it's already included in dictionaries, there's a common abbreviation "HZ" and Japanese borrowed "ハビタブルゾーン" (habitaburu zōn) in full, even if "ハビタブル" (habitaburu) is hardly used. No, AFAIK, most of the examples above didn't gain enough currency to be included but I haven't checked. --Anatoli (обсудить/вклад) 03:31, 14 January 2014 (UTC)
 * Maybe you should take a look at WT:WINW. And also, just because set is the most generic form of collection (fields, groups, rings, etc. are all sets with additional properties), doesn't mean that any set-related adjective used with the word "set" suddenly becomes idiomatic. --WikiTiki89 03:39, 14 January 2014 (UTC)
 * I know WT:WINW and I am not saying it should be included because it's in Wikipedia but I'm saying, this term is of interest to mathematicians and programmers, requires a formal definition and Wikipedia is only one of the confirmations of that, not a criterion for inclusion. Because of a complex definition and variations in definitions, it's even more of a term, than say "vegetable soup", which is understood by general public. Your knowledge of the set theory is appreciated but it doesn't make the term less important for users who are not familiar with it. --Anatoli (обсудить/вклад) 03:54, 14 January 2014 (UTC)
 * It has a formal mathematical definition at countable and uncountable. I don't see why we need to also have countable set and uncountable set to duplicate this definition. --WikiTiki89 03:59, 14 January 2014 (UTC)
 * The countable and uncountable test for sets is more involved and the full definition for each of uncountable set and countable set is less straightforward than countable / uncountable and set.
 * I'm leaving this particular topic, perhaps a vote count should decide but it seems like it should be kept for a lack of consensus. --04:07, 14 January 2014 (UTC)
 * You can count uncountable nouns: water, milk, bread (that's one, two, and three). So if I understood you correctly, your point makes no sense. --WikiTiki89 15:30, 11 January 2014 (UTC)
 * Huh? Is that an argument for keeping uncountable set or for keeping sense 2 of uncountable? —Mr. Granger (talk • contribs) 13:47, 11 January 2014 (UTC)

countable set
Similarly – a countable set is simply a set that's countable. —Mr. Granger (talk • contribs) 03:02, 10 January 2014 (UTC)
 * Delete. --WikiTiki89 03:04, 10 January 2014 (UTC)
 * Keep per Talk:free variable reasoning. The sense of "countable" or "uncountable" applied here is specific to sets. Keep also prime number, free software and other similarly formed items. --Dan Polansky (talk) 21:47, 10 January 2014 (UTC)
 * Keep. — T AKASUGI Shinji (talk) 10:21, 11 January 2014 (UTC)
 * Delete both. I think "free variable" should be kept, but this is because "free" is highly abstract and polysemous: even in mathematics it has two distinct meanings (as used in free object and, well, free variable). No such thing applies to "uncountable", which means just "not capable of being counted", to which mathematics context only adds "…using natural numbers". Given the context, the meaning is clear. Keφr 12:39, 11 January 2014 (UTC)
 * Not that it probably matters for this RFD, but IMHO the set-theoretical meaning of "countable" is quite counterintuitive; if something is countable, then a count expressed as a non-negative integer should be determinable for it; if something is infinite, then it is not countable, by my intuition anyway, contrary to the mathematician's definition. But whether the meaning is counterintuitive or not, the SoP argument for deletion can be found by those who want to find it. --Dan Polansky (talk) 13:00, 11 January 2014 (UTC)
 * "Counting" in the mathematical sense is perhaps best thought of as matching a set with another one of the same "size." — Pingkudimmi 14:27, 11 January 2014 (UTC)
 * Sure, but then a set with the cardinality of aleph 1 is also countable in this sense: it can be 1-to-1 mapped to a set with the same cardinality. So I still see "countable" (bijectively mappable to the set of positive integers) as an arbitrary and counterintuitive term, not a natural extension of the lay men's "countable". --Dan Polansky (talk)
 * I think Pingku is wrong. A "countable" set is one that can be mapped one-to-one with the set of natural numbers, in other words its any set that is the "same size" as the natural numbers. --WikiTiki89 19:05, 11 January 2014 (UTC)
 * All I was saying is that the process of counting is reimagined as a bijection to another set. Why is that wrong? The definition of "countable" is then as in the entry. It can apply to any object set, and the choice of natural numbers is perhaps arbitrary, but it also easily relates to the intuitive notion of counting. Anything that involves infinity is potentially weird. — Pingkudimmi 01:27, 12 January 2014 (UTC)
 * You were wrong about the details. It's not a bijection to a set of the same size, but rather a bijection to a specific set (i.e. the natural numbers). --WikiTiki89 03:15, 12 January 2014 (UTC)
 * Perhaps I wasn't clear enough, but the point I was getting at was that counting (which only makes sense with finite sets) is reimagined as a bijection to another (finite) set. The bijection idea is capable of being generalised to infinite sets. — Pingkudimmi 12:22, 12 January 2014 (UTC)
 * You were clear enough. You just had one of the details wrong and I corrected you. --WikiTiki89 16:17, 12 January 2014 (UTC)
 * A bijection is always between two sets of the same size. What Pingku is saying is correct, although I think it's only tangentially related to the word countable. —Mr. Granger (talk • contribs) 16:43, 12 January 2014 (UTC)
 * Wrong. A bijection is only possible with two sets of the same size. But that is only because "same size" (with infinite sets) is defined as having a "bijection". Anyway, a "countable" set is defined as one that is the "same size" (a.k.a. has a bijection with) the natural numbers. --WikiTiki89 16:47, 12 January 2014 (UTC)
 * "Counting" in both mathematical and everyday senses should be probably understood as synonymous with "enumerating", i.e. assigning natural numbers to successive items; assigning a numerical magnitude in some other way is usually called "measuring". Which makes "countable" mean "such that it can be exhausted by counting". Mathematicians just accept that the counting process may be infinite. Keφr 20:20, 13 January 2014 (UTC)
 * Keep as above. --Anatoli (обсудить/вклад) 00:15, 13 January 2014 (UTC)

Kept. bd2412 T 20:01, 25 February 2014 (UTC)