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Discussion of "fancyxra"
Comment #1:
Domain and range should be specified

Curtis W Franks (Sun Mar 2 19:49:34 2014)

If I understand this word correctly as basically the drawings that one makes in elementary mathematics of various functions, then the domain and range should be specified (and probably earlier in the definition than some terbri from, for example, pixra).


Comment #2:
Re: Domain and range should be specified

Curtis W Franks (Sun Mar 2 19:52:16 2014)

In fact, I am not even sure that the drawer needs to be specified. A graph is a graph no matter who draws it and the only aspect that may be of interest/concern is the medium in which it has been displayed (for example handmade paperandpencil or computer generated?); the authorship can be specified in other ways and is not vital to the word, I think, as a graph is an inherent mathematical entity belonging to a function.


Comment #4:
Re: Domain and range should be specified

Wuzzy (Sun Mar 2 23:34:16 2014)

krtisfranks wrote: > In fact, I am not even sure that the drawer needs to be specified. A graph > is a graph no matter who draws it and the only aspect that may be of > interest/concern is the medium in which it has been displayed (for example > handmade paperandpencil or computer generated?); the authorship can be > specified in other ways and is not vital to the word, I think, as a graph > is an inherent mathematical entity belonging to a function. Let’s keep the place. As long you aknowledge that all graphs have a drawer, there is no harm done by keeping the place. If you just do not care about a drawer, just don't mention it when using the lujvo. Why I say this: It makes the lujvo more regular, which is a plus. Also, the drawer place is the last one, so it doesn’t get in the way. But if you can show me that the a drawer _does not apply_ (this is more than just “I don’t care”) to a graph, then I may be convinced that this place better be deleted. To me, all pictures somehow have someone (or something) to draw it. So why not graphs, too?


Comment #5:
Re: Domain and range should be specified

Curtis W Franks (Mon Mar 3 01:21:32 2014)

Wuzzy wrote: > krtisfranks wrote: > > In fact, I am not even sure that the drawer needs to be specified. A > graph > > is a graph no matter who draws it and the only aspect that may be of > > interest/concern is the medium in which it has been displayed (for > example > > handmade paperandpencil or computer generated?); the authorship can be > > specified in other ways and is not vital to the word, I think, as a > graph > > is an inherent mathematical entity belonging to a function. > Let’s keep the place. As long you aknowledge that all graphs have a > drawer, there is no harm done by keeping the place. If you just do not > care about a drawer, just don't mention it when using the lujvo. > Why I say this: It makes the lujvo more regular, which is a plus. Also, > the drawer place is the last one, so it doesn’t get in the way. > But if you can show me that the a drawer _does not apply_ (this is more > than just “I don’t care”) to a graph, then I may be convinced that > this place better be deleted. > To me, all pictures somehow have someone (or something) to draw it. So why > not graphs, too?
Well the parabola of x^2 (over any specified domain and range) is precisely the same and exists always. It is much like the unit circle centered at the origin in R^2 : it just is, independent of any drawer. In fact, any drawing of these objects is actually either a complete and ideally perfect expression thereof or not actually a representation of them unless we are to understand that errors should be ignored; in the latter case, the picture is actually of another object. But I suppose that the issue here is one of English. If we follow the meaning.of "graph" as used by mathematicians who use the term this way (which is a somewhat limited application), then the picture is actually indistinguishable from the exact object (set); but if we are to understand it as a representation of the graph, then it may be imprecise and the drawer is possibly important.
Pedantically, just so we are clear, a function actually cannot be drawn; only its graph/representation (trace) can be drawn. For example, x^2 cannot be drawn but a parabola can be (arguably).
What about the other proposed terbri?


Comment #9:
Re: Domain and range should be specified

Wuzzy (Mon Mar 3 16:01:37 2014)

Okay, to clarify: I clearly interpret the word “graph” here as “graphical representation”. To say a graph of a function has to be perfect, otherwise its not a graph is not practical to me. This would automatically disqualify any drawing by hand. Also graphs on a, let’s say, LCD monitor are not perfect, because of the pixels. You always have this tiny error. To say a graph *must* be perfect would disqualify all these images. So I still think the current definition of fancyxra is pretty good and practical and does not need to be changed.
If you want to interpret “graph” in a strict mathematical sense (whatever that may be), I’d suggest to create a new lujvo, because I think you mean something different than I think. Maybe a new lujvo could settle these disputes, hopefully.






Comment #3:
Re: Domain and range should be specified

Wuzzy (Sun Mar 2 23:27:49 2014)

krtisfranks wrote: > If I understand this word correctly as basically the drawings that one > makes in elementary mathematics of various functions, then the domain and > range should be specified (and probably earlier in the definition than > some terbri from, for example, pixra). I think the lujvo is good right now and does not need to be changed. This is because the domain and range are already places in fancu, and all funca2, funca3 and funca4 are all dependent on funca1. Read <http://dag.github.io/cll/12/6/> for the concept of dependent places. The main reasoning for this is of redundancy. And I think it makes much sense and that it should be used as often as possible.
You could get the domain and range by the funca place, with relative clauses, for example: “ko'a fancyxra lo fancu poi XXX” where “XXX” can be replaced by something to further spefify the function.


Comment #6:
Re: Domain and range should be specified

Curtis W Franks (Mon Mar 3 01:32:29 2014)

Wuzzy wrote: > krtisfranks wrote: > > If I understand this word correctly as basically the drawings that one > > makes in elementary mathematics of various functions, then the domain > and > > range should be specified (and probably earlier in the definition than > > some terbri from, for example, pixra). > I think the lujvo is good right now and does not need to be changed. > This is because the domain and range are already places in fancu, and > all funca2, funca3 and funca4 are all dependent on funca1. > Read <http://dag.github.io/cll/12/6/> for the concept of dependent places. > The main reasoning for this is of redundancy. And I think it makes much > sense and that it should be used as often as possible. > > You could get the domain and range by the funca place, with relative > clauses, for example: > “ko'a fancyxra lo fancu poi XXX” where “XXX” can be replaced by > something to further spefify the function.
But that is actually a different function. x^2 defined on the interval [1,1] id a completely (well, not "completely", but very) different beast from x^2 defined on the entirety of the real numbers. Even though the traces may be the same, the underlying functions are not, which is an important distinction. The graph is some subset of the trace of a function, not the trace of a restriction of that function (even though they "appear" to amount to the same thing). Additionally, in computer programming, such as with TI calculators or Mathematica, the plot range and plot domain parameters are aspects of the plot and not of the function being plotted (which is correct usage); if Lojban is going to be compatible with these computer languages, it must have those parameters specified in its word for "graph" ("plot").
Example: I can plot log(x) on the interval [e,e], but log itself is not defined for any x ≤ 0 and there is no clean way to make it so defined; your proposal seems to be incompatible with this truth. (Note: I fell into a bad English habit. What I should have said is that the trace of log is a subset of R^2, not that I can plot it.)



Comment #8:
Re: Domain and range should be specified

Curtis W Franks (Mon Mar 3 01:40:25 2014)

I would also argue that fancu1 is more dependent on the other terbri than on the reverse, but truly they are interrelated and that is not the main point of the argument anyway. The plot of the function is expressed in a certain set but is independent of the set of definition of the function (which by the way better exhibits the dependency of the terbri, since the function and its domain specify the range, for example).





