Talk:Power set

message: I think it would be very useful for someone to include
# the reason the power set was developed
# the way power sets are used in practice or in higher math
# and how the power set relates to other topics
unfortunately, i don't know enough about power sets to even begin to write about these things. I would personally be appreciative of anyone wanting to add those. Fresheneesz 01:55, 4 November 2005 (UTC)
replies: text: You raise excellent points. Unfortunately I probably won't get to them soon. Anyone else who's interested might point out the way the set of all real numbers can be coded up by the powerset of the naturals, and might discuss how, without the powerset axiom, we can't prove the existence of uncountable sets. See also Hartogs number. --Trovatore 03:00, 4 November 2005 (UTC)
thread_title: application and use

message: ℘ (U+2118 SCRIPT CAPITAL P) redirects here, but it seems to also be used for Weierstrass's elliptic functions. Should there be a disambig page at ℘ instead? --Abdull 20:22, 7 June 2006 (UTC)
replies: text: Would be a good idea I would think. Oleg Alexandrov (talk) 05:13, 8 June 2006 (UTC)
replies: text:  I think it should be removed from here altogether and dump the disambig page. ℘ is really only used for the power set by people who don't know how to get a script looking P in LaTeX any other way. (At least, that has been my experience with it.) It's simply not the right symbol. Steve Checkoway (talk) 07:54, 21 June 2009 (UTC)
replies: text:  I agree that this is a LaTeX error and doesn't belong here. I have never seen any published work using \wp for the power set. I have therefore removed it. JordiGH (talk) 16:27, 7 July 2022 (UTC)
thread_title:  ℘ 

message: This page needs a formal definition of a power set.  Perhaps P(S)={x\subseteq S}.
InformationSpace 03:21, 12 February 2007 (UTC)
replies: text: I don't see the need, as long as the definition is correct and clear.  This is not a set-theoretical treatise (or is it?). Zaslav 10:03, 22 March 2007 (UTC)
thread_title:  Formal definition of a Power set 

message: I suggest the notation {0,1}S be de-emphasised.  It is technically incorrect, since it really means a set of functions.  Yes, they are equivalent, but they are not the same, and often that is important.  I removed it from the introduction, but not from the special notation section since it may be used sometimes in the literature. Zaslav 10:07, 22 March 2007 (UTC)
thread_title:  Notation

message: My office mate and I have both independently needed to use the notion of the set of all finite subsets of a set, and I was surprised there didn't seem to be an article on it or a mention of it in this article.  PlanetMath suggests a convention on notation for it.  Is there notation for it that is as standard as for ordinary power sets?  Somebody want to incorporate this notion into this and/or another article? --pfunk42 (talk) 20:04, 4 August 2008 (UTC)
replies: text: There's no notation that's as standard, no. But I think [A]^{<\omega} is fairly standard for the set of all finite subsets of A. --Trovatore (talk) 20:11, 4 August 2008 (UTC)

text: Also \mathcal{P}_{fin}(A). — Carl (CBM · talk) 20:24, 4 August 2008 (UTC)
replies: text:  Yikes! Surely you mean \mathcal{P}_{\mathit{fin}}(A). Steve Checkoway (talk) 07:55, 21 June 2009 (UTC)
replies: text:  Based on the notation for subsets of limited cardinality in the article, we already effectively have a notation for this: \mathcal{P}_{\aleph_0}(A).  But is there a prose name?  "Finite power set" might work as an informal term to tell some people what you mean, but it's inaccurate - unless A is finite, then both the power set and this subset are in fact infinite sets. — Smjg (talk) 15:50, 14 March 2015 (UTC)
thread_title:  Finite power set 

message: Hello. In my view, the section "Algorithms" was too long, making the article a little unbalanced. (In my experience, the field of "algorithms for computing powersets" is tiny in the general subject of "powersets".) I have removed the illustration of the algorithm, because the description of the algorithm is clear and sufficient. I apologise in advance to J R Spriggs, who undid my earlier action, perhaps with good reason. Another thing: it would be good if someone could provide a reference for the algorithm (I can't find one). Sam (talk) 10:23, 30 October 2008 (UTC)
replies: text: Someone put an implementation for the algorithm on the page. As discussed above, it doesn't really belong. I've moved the source code here until a more appropriate place for it is found. Sam (talk) 09:25, 14 April 2009 (UTC)
thread_title:  Algorithms 

message: Concerning the representation of Boolean algebras as subalgebras of power-set Boolean algebras, what is the intended meaning of the strange parenthetical remark "though this is not always a particularly illuminating representation of an infinite Boolean algebra"?  That there exist unilluminating representations, or that there exist Boolean algebras that have no illuminating representation, or that there exist people who don't always find such representations illuminating?  If the first then what does this have to do with Boolean algebras?  Do there exist any algebraic structures which have no unilluminating representations?  If the second, what's an example?  Every example I could think of has a representation as a field of sets that I found illuminating.  If the third, again what does this have to do with Boolean algebras, this has to be true for every kind of algebraic structure.  --Vaughan Pratt (talk) 13:08, 8 May 2009 (UTC)
replies: text: I didn't write it, and I don't mind removing it. My guess is that they are saying that because of the nature of the representing algebra (it's a subset of a powerset algebra of ultrafilters, after all), the representation may not be very useful for obtaining results about the original Boolean algebra. But this is just part of the nature of the representation, so the parenthetical remark seems to be mostly useless. I can think of parallel case in other areas where there are general representations, but they are not very often useful. — Carl (CBM · talk) 13:25, 8 May 2009 (UTC)
thread_title: Not illuminating?

message: User:AMenteLibera wrote <<Please add demonstration - one can be found in the italian wiki at Insieme delle parti>> in the section Power set#Properties. I think that request is more appropriate here on the talk page. There is a sketch argument already, in the footnote -- is that enough? or should we include a proof... ComputScientist (talk) 18:08, 4 November 2011 (UTC)
thread_title:  Request for demonstration 

message: I've just added to the properties section a somewhat colloquial explanation why the cardinality is exponential. It is true that the very next section gives essentially the same information. But that pre-existing presentation is much more technical than the version I inserted, and I think that readers with less mathematical sophistication will, despite their lack of expertise, be interested to know why it's exponential.
Nevertheless, the article does contain at this moment two successive versions of the same information that are merely expressed at distinct levels of technical detail. How do others think we should proceed?—PaulTanenbaum (talk) 14:51, 5 April 2012 (UTC)
thread_title:  Redundance about cardinality? 

message: What is the source of the "Subsets of limited cardinality" section?
Should not \mathcal{P}_{\kappa}(S) mean the set of subsets of S of cardinality less than or equal to κ?
Is \mathcal{P}_{\leq \kappa}(S) also a commonly used notation?
utapyngo (talk) 08:43, 21 November 2012 (UTC)
thread_title:  Notation for powersets of limited cardinality 

message: why is this included in the "binary operations" section of Template:Set_theory? Adavies42 (talk) 22:06, 17 December 2012 (UTC)
replies: text: Good catch — I've removed it. --Trovatore (talk) 22:08, 17 December 2012 (UTC)
thread_title:  binary operation? 

message: The Power Set describes the set generated by the Kleene star operation, but neither page references the other. I suggest making the relationship explicit. SMesser (talk) 21:47, 1 December 2014 (UTC)
replies: text: The Kleene star is the set of ordered finite sequences made with elements from a given set.  The powerset is the set of unordered subsets, and they don't have to be finite.  It's true that the operations have some things in common, but I don't immediately see any relationship so compelling that it burns to be stated here.  (I wouldn't oppose adding it to "see also".) --Trovatore (talk) 15:51, 2 December 2014 (UTC)
thread_title:  Link to Kleene Star page 

message: We may as well mention binary trees, hexadecimal numbers and 32bit CPUs here, because, lets face it, 2^n appears everywhere. Good idea would be linking to 2^n article, and from there linking to all the relevant articles about powers of two, including binomial stuff.
-NikitaSadkov (talk) 00:13, 17 October 2018 (UTC)
thread_title:  "Relation to binomial theorem" seems excessive 

message: # analyze set theories of physics (nowadays are impossible because physics is incomplete, but add links on the subject)
# after you add set theories of physics; as a metalogical elaboration of cosmogony through the prism of set theory (even that is not possible nowadays; but add all the links; not here; make a page. Don't blame me for writing here and not on the non-existing page.)
Zero doesn't exist (the average of some set or some qualities can be zero, but not any specific material something). The null set exists. The universe exists.
::It makes no sense to start with cosmogony. Mention set theories of physics.  — Preceding unsigned comment added by 2A02:587:4115:1000:4005:4380:AB99:AB8C (talk) 23:07, 18 July 2019 (UTC)
thread_title:  ''make page'': [[Set theory and cosmogony]] 

message: I noticed that the article tends to use the markup  for the power set-P, which renders as .  However, this doesn't look anything like the LaTeX equivalent: \mathcal{P} (for me).  The wikicode version simply looks like a funny sans-serif roman P.  I've been meaning to deal with stuff that uses  for a while now, but haven't gotten around to it.  WP:VPT or WT:WPM might be a better place for this, but I thought I'd just try quick sense if other people have the same issue before going elsewhere.  –Deacon Vorbis (carbon • videos) 14:36, 27 October 2019 (UTC)
replies: text: The two mathcal P's look similar on my system; the main difference is that the wikicode one has a horizontal stroke at the bottom, which is not present in the latex one.  They are certainly recognizable as the same symbol.  --JBL (talk) 13:28, 18 December 2019 (UTC)
thread_title:  Which P to use... 

message: In the current version Special:PermaLink/986826045 there is a note in the lead section, defined with <ref group=note>. It got its number 1. in the note group, but it's displayed right above a 1. reference defined with the default group – see Special:PermaLink/986826045#Notes.
That's because both reflists are inserted in the same Notes section. I would like to split the section into Notes and References, but the  References section exists already and it contains bibliography!
How should I clean up that mess? --CiaPan (talk) 09:49, 3 November 2020 (UTC)
replies: text:  Solved by splitting the Notes section into Notes & Reference and renaming previous References section to Bibliography: Special:Diff/986874963. --CiaPan (talk) 14:33, 3 November 2020 (UTC)
thread_title:  Notes and References and ...?