defining a set

[ravas]

linji

x1 is a line/among lines (1-dimensional shape/form) defined by set of points x2.

----

How do we define a set?

la ky. linji la .abu. .e la .ebu.

Is this correct?

----

Can we define the set prior to using linji?

la .abu. .e la .ebu. cmima da goi ko'a
.i la ky. linji ko'a

Is this correct?

----

The use case is instructions for geometric construction.

.a'o

[Pierre Abbat]

On Wednesday, December 17, 2014 23:19:06 ravas wrote:
> *linji*

>
> x1 is a line/among lines (1-dimensional shape/form) defined by set of
> points x2.
>
> ----
>
> How do we define a set?
>
> la ky. linji la .abu. .e la .ebu.
>
> Is this correct?

{la .ky. linji} means "K's Line", as a name. I think you mean {ky. linji .abu.
e .ebu}.

{ky. linji .abu. ce .ebu} is correct, if A and E are points. {ky. linji .abu.
e .ebu} implies that A and E are (possibly different) sets of points, each of
which defines the line K.

> Can we define the set prior to using linji?
>
> la .abu. .e la .ebu. cmima da goi ko'a
> .i la ky. linji ko'a
>
> Is this correct?

Again drop {la}. There are infinitely many sets that contain A and E (and other
things), some of which do not define lines, so no.

Pierre

--
Jews use a lunisolar calendar; Muslims use a solely lunar calendar.

[ravas]

On Thursday, December 18, 2014 5:17:42 AM UTC-8, Pierre Abbat wrote:

{ky. linji .abu. ce .ebu}

mi pu djica .ui
 

There are infinitely many sets that contain A and E (and other
things), some of which do not define lines, so no.

Can we use [po'o] to say these are the only members of the set?

abu. e .ebu. po'o cmima da goi ko'a
.i ky. linji ko'a

---

ki'esai .io

[Ian Johnson]

Technically this attaches the {po'o} to {.ebu} which is undesirable. Moreover there is a semantic problem with binding an existential variable to a constant variable. (It isn't so bad when there is only one layer of quantification but it is catastrophic otherwise.) But there's a simpler approach:

{.i ky linji .abu ce .ebu}

or if you want a variable:

{.i ky linji ko'a goi .abu ce .ebu}

or if you want the referents first:

{.i ky linji .abu ce .ebu vu'o goi ko'a}

Using {cmima} precisely winds up being awkward because you have to do something like:

{.i ca'e ro da zo'u da cmima ko'a .i jo da cmima .abu ce .ebu}

mi'e la latro'a mu'o

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[ravas]

On Thursday, December 18, 2014 2:11:36 PM UTC-8, Ian Johnson wrote:

Using {cmima} precisely winds up being awkward because you have to do something like:

{.i ca'e ro da zo'u da cmima ko'a .i jo da cmima .abu ce .ebu}

 

Awkward but interesting... ;D

I will be using {.i ky linji .abu ce .ebu} most of the time;
however, I may need to refer to 2 points repeatedly.
In that situation it would be convenient to refer to them with one word.
Mostly I'm just curious about what is possible. :D

Can we accomplish this using something other than cmima?

What about:

.abu. ce .ebu. goi ko'a zasti

or

ko'a smugau .abu. ce .ebu.

or

.abu. ce .ebu. du ko'a

---

kie'cai .io

[Ian Johnson]

In the first case you need {vu'o} to make the {goi} apply to the whole set. The second one is technically OK, though {du} has its own problems in general.

mi'e la latro'a mu'o

--

[ravas]

On Thursday, December 18, 2014 5:15:35 PM UTC-8, Ian Johnson wrote:

In the first case you need {vu'o} to make the {goi} apply to the whole set. The second one is technically OK, though {du} has its own problems in general.

i'o do jarco zo vu'o

ni'o .ui mi pu balcli

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ki'ecai .io