Talk:uncountable set

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Latest comment: 10 years ago by BD2412 in topic uncountable set
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RFD 2014

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The following information passed a request for deletion.

This discussion is no longer live and is left here as an archive. Please do not modify this conversation, but feel free to discuss its conclusions.


uncountable set

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An uncountable set is a set that's uncountable, nothing more and nothing less. —Mr. Granger (talkcontribs) 03:01, 10 January 2014 (UTC)Reply

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 (talkcontribs) 22:14, 10 January 2014 (UTC)Reply
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)Reply
Sense 5 of single is specific to people - does that mean we should have an entry for single person? —Mr. Granger (talkcontribs) 22:56, 10 January 2014 (UTC)Reply
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 "<adjective> <noun>". --Dan Polansky (talk) 23:15, 10 January 2014 (UTC)Reply

Similarly – a countable set is simply a set that's countable. —Mr. Granger (talkcontribs) 03:02, 10 January 2014 (UTC)Reply

  • Delete. --WikiTiki89 03:04, 10 January 2014 (UTC)Reply
  • 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)Reply
  • Keep. — TAKASUGI Shinji (talk) 10:21, 11 January 2014 (UTC)Reply
  • 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 w:free object and, well, w: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)Reply
    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)Reply
    "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)Reply
    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)Reply
    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)Reply
    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)Reply
    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)Reply
    You were clear enough. You just had one of the details wrong and I corrected you. --WikiTiki89 16:17, 12 January 2014 (UTC)Reply
    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 (talkcontribs) 16:43, 12 January 2014 (UTC)Reply
    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)Reply
    "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)Reply
  • Keep as above. --Anatoli (обсудить/вклад) 00:15, 13 January 2014 (UTC)Reply

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