User:Jshflynn/Ideas:Dictionary search

It seems most definitions could be structured like this:

Definiens

 * $(R, \oplus, \otimes)$ is a ring.
 * $(R, \oplus, \otimes)$ is not the null ring.
 * $(R, \oplus, \otimes)$ has no proper zero divisors.
 * $\otimes$ is commutative.

Definiendum

 * $(R, \oplus, \otimes)$ is an integral domain.

Definiens

 * $(\Omega, \Sigma)$ is a measurable space.
 * $\mu$ is a measure on $\Sigma$.

Definiendum

 * $(\Omega, \Sigma, \mu)$ is a measure space.

Possible thoughts
I would quite like to do away with word "let". If only the world knew what definiens and definiendum meant.

Alternatives:

definiens: Build

definiendum: Encapsulate/Label/Finish

Also I'm pretty sure having the conditions listed like that would be good for searching for a word. You could create alternative definitions on the fly by "unpacking" the bullet points in the definiens.

Will think about this some more...


 * With my limited knowledge of Latin, I'd say 'definiens' means "what is being used to define", and 'definiendum' "what is being defined". --Lord_Farin (talk) 14:31, 8 November 2012 (UTC)
 * Also, I'd have a difficult time writing Definition:Pullback (Category Theory) in this format. But that may be just me. --Lord_Farin (talk) 14:33, 8 November 2012 (UTC)
 * Excellent point. I have now qualified my statement by saying "most definitions". I don't really hate the word "let" btw it's just like "dim" or "var" in a programming language. I just proposed this for the searching possibilities.


 * Definiens and Definiendum should of course be added to the dictionary. But I am strongly against structuring all definition pages using those terms. While I'm in favour of defining concepts like "injection" and "surjection" by their technical terms rather than the kindergarteny "one-one" and "onto" (you know exactly where we stand) I see no merit in making the language that glues the mathematics together any more complicated than it already is.


 * "Let" is a universally understood shorthand for "I'm about to define something here, listen carefully" and, while it may come across as a little old-fashioned, it works really well and I would not like to see it replaced with Latin that I myself only understand because I'm widely read. There is already a contributor here who is keeping a dictionary of the English slang I use, swelpme - we really don't need an added level of obscurantism.


 * If you are fed up writing "dim" and "var" in your programming language of choice, I suggest you upgrade your skills to a real language :-) --prime mover (talk) 20:21, 8 November 2012 (UTC)


 * Very funny PM. I do some Java when time permits (write now I'm trying some PHP). I just used "dim" and "var" because I thought they were quite common among PLs.


 * Of course I don't really want Definiens and Definiendum to replace what we have here as that would be ridiculous. I thought the bullet points idea might have interested you though if you ever wanted to create a "reverse dictionary" for mathematics. Remember when you wondered about whether or not a concept had been researched to death already only not knowing how to find out how? Well this could be a step in that direction :) --Jshflynn (talk) 21:09, 8 November 2012 (UTC)


 * I've got nothing against structure - I just don't like definiens and definumimumuanamanah dee dee, de dee dee ... as for bullets, other contributors do not like bullets. The current standard arrangement: let ..., let..., let..., then ... seems an adequate compromise between human readability and computer readability. At least we never fell into the Websterian habit of trying to define everything about an object in one tortuous sentence. --prime mover (talk) 21:23, 8 November 2012 (UTC)


 * Webster's does that? I thought they were revered. I will have to investigate that further. I have always been fascinated by dictionaries and reference works. I highly recommend the following video to anyone else who is:

OED 80th anniversary talk


 * It contains segments about the history of the OED and details of how it all works behind the scenes. I think I'm quite fine with the "let then" structure now. I just need to work on getting "iff" and "xor" in English for now :D --Jshflynn (talk) 21:45, 8 November 2012 (UTC)