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Re: [lojban-beginners] how to use {fancu}?


On Wed, Sep 17, 2014 at 3:35 AM, Gleki Arxokuna <gleki.is.my.name@gmail.com> wrote:
How to say e.g. "f(x) = (x + 1) (x − 1)" ? Should I use {fancu} for that? If not how to use {fancu}?
I want an example with all places of {fancu} filled.

fancu = x1 is a function/single-valued mapping from domain x2 to range x3 defined by _expression_/rule x4.


E.g "f(x) = (x + 1) (x − 1)" where x>1

fy fancu xy lo du'u xy zmadu li pa vau li vei xy su'i pa ve'o pi'i vei xy vu'u pa ve'o ?

We need to distinguish three cases:

(1) example of what the gimste says it means
(2) example of what "fancu" ought to mean
(3) example of actual usage

If you want (1), you could say:

 fy fancu lo'i mrena'u poi zmadu li pa lo'i mrena'u poi zmadu li no me'o vei xy su'i pa ve'o pi'i vei xy vu'u pa ve'o

You want "me'o", not "li", for an _expression_. I'm assuming you meant it as a function on the reals and not, for example on the integers. The domain of the function is the set of values for which the function is defined. The range is the set from which the function takes its values. In this case it could also have been all the reals, even though the function never takes negative values. lo'i mrena'u poi zmadu li no is the image, which has to be included in the range. It doesn't say anywhere that "xy" is the variable that will take its values from the domain, but using x as a variable is of course a very common convention.

As for (2): It doesn't really make a lot of sense to me to have a place for _expression_ x4 in addition to a place for the function. It's as if "klama" was defined as "x1 goes to x2 ... and has name x6". The place for the range is also redundant. It's as if "jalge" was defined as "x1 is the result of x2 among potential results x3", or something like that. "fancu" ought to have just two places: "x1 is a function of x2". Your example would be: "fy pe xy du li vei xy su'i pa ve'o pi'i vei xy vu'u pa ve'o", which doesn't use "fancu", but you could also say fy fancu xy noi mrena'u gi'e zmadu li pa". A more general use would be:
 
 lo jdima be lo seldi'a cu fancu lo ni sy se sabji jo'u lo ni sy se cpedu
 "The price of a good is a function of its supply and demand."

Finally (3), usage, is all over the place. An example from Tatoeba (just because it's the first hit for "cu fancu" that I get from Google):

  ro da poi fancu lo nuncfa cu fancu lo nunfa'o
  Whatever is subject to origination is all subject to cessation.

But I don't really see how "fancu" can be "subject to". To me that says that every thing that depends on a start, depends on having (or being?) an end. "Being subject to" is more like "lifri". I would say: "ro da poi lifri lo ka cfari cu lifri lo ka tolcfa".

mu'o mi'e xorxes

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