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.