Talk:Ordered pair

message: Can the sequence triple, quadruple, etc. be extrapolated?? Let me see:
*2. pair
*3. triple
*4. quadruple
*5. quintuple
*6. sextuple
*7. septuple
*8. octuple
*9. nonuple
*10. decuple
*11. undecuple
*12. duodecuple
*13. tredecuple
*14. quattuordecuple
*15. quindecuple
*16. sexdecuple
*17. septendecuple
*18. octodecuple
*19. novemdecuple
*20. vigintuple
*30. trigintuple
*40. quadrigintuple
*50. quinquagintuple
*60. sexagintuple
*70. septuagintuple
*80. octogintuple
*90. nonagintuple
*100. centuple
*125. quasquicentuple
*150. sesquicentuple
*175. terquasquicentuple
*200. bicentuple
*300. tercentuple
*400. quatercentuple
*500. quincentuple
*1000. milluple
*10^6. milliontuple
66.245.6.12 00:50, 25 Aug 2004 (UTC)
thread_title:  Extrapolating the tuple sequence 

message: I replaced the text In the usual  Zermelo-Fraenkel formulation of set theory including the axiom of regularity, ordered pairs (a, b) can also be defined as the set {a, {a, b}}. However, the axiom of regularity is required, since without it, it is possible to consider sets x and z such that x = {z}, z = {x}, and x ≠ z. Then we have that
:(x, x) = {x, {x, x}} = {x,{x}} = {x, z} = {z, x} = {z, {z}} = {z, {z, z}} = (z, z)
although we want (x,x) ≠ (z,z).
by a few examples of possible other definitions, plus reasons why they are not used. Aleph4 13:44, 18 Feb 2005 (UTC)
thread_title:  Other pairs 

message: Is the Wiener definition actually
:(x,y)=\{\{\{x\},\emptyset\},\{\{y\}\}\}?
::Yes.
Why did he not use 
:(x,y)=\{\{\{x\},\emptyset\},\{y\}\}? --NeoUrfahraner 06:13, 22 March 2006
::Because he introduced his definition the the framework of Russell and Whitehead's theory of types. There all elements in a class must be of the same type, namely one less than the type of the class (they are elements of). Now if x and y are of, say, type n, then {x} and {y} would be of type n+1, and {{x}, 0} would be of type n+2. Now putting {{x}, 0} and {y} in the same class would mean a "type clash". Hence we have to use { {y} } --which is also of type n+2-- instead of {y}.</nowiki> —Preceding unsigned comment added by 91.59.209.222 (talk) 00:09, 3 December 2007 (UTC)
thread_title:  Wiener definition 

message: in the 2nd paragraph it says:
"The notion of ordered pair is crucial for the definition of Cartesian product"
in the paragraph "morse definition" it then says
(x,y)=\{x \times \{0\}\}\cup\{y \times \{1\}\}
which uses a cartesian product. so an ordered pair is defined in terms of a cartesian product which is defined in terms of an ordered pair which is defined in terms of a cartesian product etc
12:38, 7 April 2007 (UTC)
thread_title:  definition of caartesian product uses ordered pair, but Morse definition of ordered pair uses cartesian product 

message: As the Kuratowski definition defines an ordered pair (a,b) as the set (a,b)= {{a}, {a,b}}, what if a=b? Quote: "However, for purposes of foundations of mathematics it has been considered desirable to express the definition of every type of mathematical object in terms of sets". That means the 'set' {a,b} isn't a set but a multiset. Am I correct or just running in circles?
:If a=b, then (a,b)= \{\{a\}\}, i.e. if the set defining the pair has only one element, then both components of the ordered pair are equal. I see no need for a multiset. --NeoUrfahraner 10:28, 28 September 2007 (UTC)
thread_title:  Set vs Multiset? 

message: "In mathematics, a pair (a,b) is ordered if (a,b) is not equivalent to (b,a)."
Isn't that only true if it is also true that a is not equivalent to b?- (User) WolfKeeper (Talk) 00:15, 24 February 2008 (UTC)
replies: text: The person who made this edit appeared to be trying to clarify the introduction, which currently seems to be rather technical.  The addition doesn't seem to handle the possibility that a and b are the same thing.  I've reverted the edit, since I don't see an obvious way to make the introduction clearer. Michael Slone (talk) 03:26, 24 February 2008 (UTC)
replies: text:  I attempted some rewording to the idea clearer and less technical (or at least easier to read...).  Although probably more understandable, I'm not sure if it's rigorous enough.  We might want a multi-paragraph lede to explain the concepts in more detail.  —AySz88\^-^ 08:21, 2 March 2008 (UTC)
thread_title:  Mistake in introduction? 

message: It would be nice to provide a proof for the simple treatment [(x,y)={x,{x,y}}] as this is the definition given in many introductory math texts.  Also, I remember somewhere seeing another definition of the ordered pair (maybe in Quine's Philosophy of Logic?) such that:
The ordered pair (x,y) = {x,{y}}.  I'm probably missing something (and perhaps this definition runs into difficulties with iteration) -- but I don't think I saw that definition in the article.  Thoughts?  —Preceding unsigned comment added by 169.231.34.169 (talk) 02:33, 30 June 2008 (UTC)
thread_title:  Another Definition and Proofs 

message: Can we delete the "reverse definition"? Its completely identical to the "regular" definition, and the distinction is only syntactic  —Preceding unsigned comment added by AbnormallyNormal (talk • contribs) 14:49, 3 September 2008 (UTC)
thread_title:  Redundancy 

message: I wish to draw everyone's attention to the following article:
Dana Scott and McCarty, Dominic (2008) "Reconsidering Ordered Pairs," Bulletin of Symbolic Logic 14(3): 379-97.
The entry should mention this article in some way, and incorporate a bit of its rich content.111.69.249.90 (talk) 12:42, 25 October 2010 (UTC)
thread_title: Recent article by Dana Scott and McCarty

message: There is some mixture of math formatting on this article. For simple ASCII math (anything with just letters, punctuation, and subscript/superscripts), I propose we just use HTML formatting and lose all the "math" tags, many of which are showing up as images for me. — Carl (CBM · talk) 13:58, 4 April 2011 (UTC)
replies: text: Agree. HTML is  preferred where  possible. Paul August ☎ 14:21, 4 April 2011 (UTC)

text: I also agree. There is nothing on this page that requires math tags, and that is not likely to change. Hans Adler 14:24, 4 April 2011 (UTC)
thread_title:  Math formatting 

message: I'd like to nominate the first sentence of this article as the most obscure definition of the most elementary concept.  Really, someone who's mathematical knowledge is sufficiently slight that they don't know what "ordered pair" means will not have a chance of understanding the first sentence.
Having said that, I'll try to fix it. McKay (talk) 06:44, 2 September 2011 (UTC)
thread_title:  intro 

message: Does it make sense to use the Kuratowski ordered pair definition for proper classes in Ackermann Set Theory resp. its extension ARC? 
If so, shouldn't this also be mentioned?
-- 132.231.198.38 (talk) 15:32, 22 June 2012 (UTC)
thread_title:  Ackermann set theory + proper classes 

message: In the formulas given under Kuratowski definition for extracting the first and second coordinates, what is the purpose of the outermost Union? I had difficulty finding a definition of what unary union does in all cases.  Is the idea to "remove an outer layer of set enclosure"?  Ie: {a} --> a?  But if a is not a set, but a value such as 6, will this succeed?  I expected the result of a union operation to be a set. Gwideman (talk) 13:02, 28 August 2012 (UTC)
replies: text: Everything, including "6", that can be put in a set is a set. --JBL (talk) 13:45, 28 August 2012 (UTC)
thread_title:  Coordinate extraction formulas 

message: The notation {(a, b)} is ambiguous. It can mean either the singleton whose single element is (a, b) or the doubleton whose elements are (a and b). GeoffreyT2000 (talk) 02:45, 18 June 2015 (UTC)
thread_title:  Ambiguity 

message: The article says: "Also note that the short version is used in Tarski–Grothendieck set theory, upon which the Mizar system is founded."  However, under the Mizar implementation of Tarski–Grothendieck set theory, it shows that the Kuratowski definition is used.  This is a contradiction, so one of these articles must be wrong. 173.76.101.86 (talk) 02:04, 7 July 2016 (UTC)
thread_title:  Contradiction with Tarski–Grothendieck set theory article 

message: The section contains this text: Then the characteristic (or defining) property of the ordered pair is: Per MS:BOLD, the use of boldface for this purpose is discouraged. I propose to use Then the characteristic (or defining) property of the ordered pair is: instead. Ladislav Mecir (talk) 04:21, 21 September 2016 (UTC)
replies: text: I agree. --Bill Cherowitzo  (talk) 18:03, 21 September 2016 (UTC)
thread_title: Boldface in the "Generalities" section

message: In the Variants section of Kuratowsi's definition, the following is listed: (a,b)_{01} = \{\{a,0\},\{1,b\}\}.  It seems like this definition would not be adequate, as we would have for example (\{0,1\},b)_{01} = (\{1\},b)_{01}.  Does this pair require a custom definition of equality, or what?  — Preceding unsigned comment added by Luqui (talk • contribs) 16:47, 29 April 2018 (UTC)
thread_title:  Kuratowski "01" variant 

message: Ordered pair rectangular coordinate plane and quadrant 114.108.244.56 (talk) 20:46, 11 September 2022 (UTC)
replies: text: - I guess, you suggest to add some remarks about using ordered pairs in analytic geometry. More generally, we should have a section about typical applications of ordered pairs. Currently, the article only explains how ordered pairs can be specified and implemented, but not what they are good for. - Jochen Burghardt (talk) 07:52, 12 September 2022 (UTC)
thread_title:  Gen math