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== Untitled section ==
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== Suggestion to Solve Problems Readers Might Have Reading the 'Functions' Section of this Article ==
Can I suggest that the 'Functions' section of this article be reformulated to take advantage of the fact that a lot of the logical statements which reside inside refer to a requirement of function transitivity and that transitive relativity was already defined in the previous section on relations? I think that this change will make the article a ''lot'' easier to read.
[[User:BCG999|BCG999]] ([[User talk:BCG999|talk]]) 20:46, 17 January 2013 (UTC)
:I don’t understand the suggestion. Functions are not transitive. What do you mean by a transitive relativity?—[[User:EmilJ|Emil]] [[User talk:EmilJ|J.]] 13:05, 18 January 2013 (UTC)
::{{In5}}Sorry; I should have been more clear in stating my original suggestion. I was [[Wikipedia:Reference desk/Mathematics#January 15th#Trouble Reading an Article|having trouble reading this article's section on functions]] because some of the notation used in their description seemed confusing. This prompted me to ask about it at the [[Wikipedia:Reference desk/Mathematics|Mathematics Reference Desk]] in an ongoing discussion that you may join if you wish. I think that the people who responded to my initial post fixed any outstanding problems, but I still wanted to suggest that the first instance of this confusing notation, <math>\forall x,y,z\,(x F y \wedge x F z \rightarrow y=z)</math>, be revised to reference the fact that a similar notation had already been used in [[Implementation of mathematics in set theory#Properties and kinds of relations|the previous section]] to denote [[Transitive relation|transitive relations]]. I just wanted to know if it would be appropriate to rid the article of the confusion caused by this kind of redundancy.
::Thanks for listening,
::{{In5}}[[User:BCG999|BCG999]] ([[User talk:BCG999|talk]]) 18:19, 18 January 2013 (UTC)
:::(That was me actually, who fixed it.) The condition of transitivity, <math>\forall x,y,z\,(x R y \wedge y R z \rightarrow x R z)</math>, is quite different from functionality, apart from the superficial fact that it happens to be a Horn formula with three universal quantifiers. There is no redundancy here, and there is no sensible way to reduce one to the other. What do you find confusing about it?—[[User:EmilJ|Emil]] [[User talk:EmilJ|J.]] 18:34, 18 January 2013 (UTC)
::::{{In5}}Silly me, I must have overlooked that tiny difference and filled it in with something from my apparently-fallible memory when skimming back over it to compare the two. I hope that I didn't project too much of my own idiosyncratically-muddled thought processes into your head and would like to apologize for any inconvenience I may have caused you because of how I amreading this article to figure out how exactly I could define an <math>n</math>-tuple as a function that I can use to define a multiset as the foundation for the sample space of any probability distribution that I might have to work with as part of an assignment for my high-school probability-and-statistics class and thus don't have much experience reading formal expressions of mathematical logic. I'm doing this because I though that I might be able to describe such a sample space as a normal set and found that it might make my math easier later to do so because understand a lot of the logic behind set theory's operations. However, I soon learned that sets cannot accommodate multiple occurrences of individual event subsets of itself as required by empirical probability and the problems that I will later work through. In retrospect, maybe we should take this back to the reference desk…
::::Forgive me,
::::{{In5}}[[User:BCG999|BCG999]] ([[User talk:BCG999|talk]]) 19:33, 18 January 2013 (UTC)
::::::There’s absolutely no need to apologize.—[[User:EmilJ|Emil]] [[User talk:EmilJ|J.]] 20:43, 18 January 2013 (UTC)
:::::::Oh; okay. [[User:BCG999|BCG999]] ([[User talk:BCG999|talk]]) 19:28, 19 January 2013 (UTC)
==Confusing redirect pages: [[Formalized mathematics]] vs. [[Formalism (mathematics)]] and [[Mathematical formalism]]==
All 3 of these links point to different pages, including this page. Is [[mathematical formalism]] distinct from [[formalism (mathematics)]] in any way? [[User:Jarble|Jarble]] ([[User talk:Jarble|talk]]) 00:30, 3 April 2015 (UTC)
:Oh, it's completely different, at least in my usage. I would expect an article called ''mathematical formalism'' to be about collections of formal methods for addressing a given informal problem — for example, in the history of quantum mechanics, the wave formulation and the matrix formulation were competing mathematical formalisms, until it was shown that they were reducible to one another. At which point, I suppose, they remained competing mathematical formalisms, but competing only as to which one was more useful or more perspicacious, as opposed to which one was correct.
:On the other hand, I would expect ''formalism (mathematics)'' to be about a viewpoint in the philosophy of math, according to which mathematics is about statements formally derivable from axioms, as opposed to statements that refer to actually existing abstract objects.
:I wrote the above without checking where the ''actual'' links point, because if that's wrong, it's relatively inessential and easily corrected. I'll check after I save the page. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 00:50, 3 April 2015 (UTC)
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