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Discussion of "kancu"

Comment #1: Issues
Curtis W Franks (Sun Jan 1 08:25:23 2017)

I think that there really are two words here.

The first is "cardinality", which we already have. It is simple "x1 is the
number of elements in/cardinality of set x2". This uses on kancu2 and
kancu3 (antirespectively). This requires no counter (person doing the
counting) and is independent of the method used to count.

The second word is something along the lines of "enumerate", "tabulate",
"tally", or "count up". This is a task performed by someone (a counter) and
depends on the method. I personally think that it would be fine to
straight-up delete kancu3 for this purpose, but perhaps we should just
retool it (I am not sure how, though). Instead of trying to figure out the
cardinality of a set (kancu2), it would just be producing a running tally
of objects/divisions/units (kancu2'). In this way, it is not actually tied
to the grand total, only what has thus far been counted. This word would be
useful for estimation of the size of an army, counting coins or money
values from a purse (counting by units), or counting down in units of time
(kancu2' would just be something like "loi snidu"). In this word a new
terbri could be introduced which designates the first value from which the
counting starts; in counting down time, this would commonly be something
like "ten [seconds]". (Aside: counting down would involve li ni'u (pa) in
the units terbri.) Notice that the counter is not actually counting how
many seconds are remaining; they are starting with that knowledge and then
enumerating them in reverse order as they pass (within approximation - the
counted seconds are not perfect, nor is the original t-minus-ten mark).

Comment #2: Re: Issues
Curtis W Franks (Sun Jan 1 08:27:07 2017)

krtisfranks wrote:
> I think that there really are two words here.
>
> The first is "cardinality", which we already have. It is simple "x1 is
the
> number of elements in/cardinality of set x2". This uses on kancu2 and
> kancu3 (antirespectively). This requires no counter (person doing the
> counting) and is independent of the method used to count.
>
> The second word is something along the lines of "enumerate", "tabulate",
> "tally", or "count up". This is a task performed by someone (a counter)
and
> depends on the method. I personally think that it would be fine to
> straight-up delete kancu3 for this purpose, but perhaps we should just
> retool it (I am not sure how, though). Instead of trying to figure out
the
> cardinality of a set (kancu2), it would just be producing a running tally

> of objects/divisions/units (kancu2'). In this way, it is not actually
tied
> to the grand total, only what has thus far been counted. This word would
be
> useful for estimation of the size of an army, counting coins or money
> values from a purse (counting by units), or counting down in units of
time
> (kancu2' would just be something like "loi snidu"). In this word a new
> terbri could be introduced which designates the first value from which
the
> counting starts; in counting down time, this would commonly be something
> like "ten [seconds]". (Aside: counting down would involve li ni'u (pa) in

> the units terbri.) Notice that the counter is not actually counting how
> many seconds are remaining; they are starting with that knowledge and
then
> enumerating them in reverse order as they pass (within approximation -
the
> counted seconds are not perfect, nor is the original t-minus-ten mark).


I run into this problem frequently and it basically makes the word, as
presently defined, useless. It cannot be used for either of these meanings
because it has the other meaning inappropriately but unavoidably wrapped up
in it.

Comment #3: Re: Issues
gleki (Sun Jan 1 09:33:57 2017)

krtisfranks wrote:
> I think that there really are two words here.
>
> The first is "cardinality", which we already have. It is simple "x1 is
the
> number of elements in/cardinality of set x2". This uses on kancu2 and
> kancu3 (antirespectively). This requires no counter (person doing the
> counting) and is independent of the method used to count.
>
> The second word is something along the lines of "enumerate", "tabulate",
> "tally", or "count up". This is a task performed by someone (a counter)
and
> depends on the method. I personally think that it would be fine to
> straight-up delete kancu3 for this purpose, but perhaps we should just
> retool it (I am not sure how, though). Instead of trying to figure out
the
> cardinality of a set (kancu2), it would just be producing a running tally

> of objects/divisions/units (kancu2'). In this way, it is not actually
tied
> to the grand total, only what has thus far been counted. This word would
be
> useful for estimation of the size of an army, counting coins or money
> values from a purse (counting by units), or counting down in units of
time
> (kancu2' would just be something like "loi snidu"). In this word a new
> terbri could be introduced which designates the first value from which
the
> counting starts; in counting down time, this would commonly be something
> like "ten [seconds]". (Aside: counting down would involve li ni'u (pa) in

> the units terbri.) Notice that the counter is not actually counting how
> many seconds are remaining; they are starting with that knowledge and
then
> enumerating them in reverse order as they pass (within approximation -
the
> counted seconds are not perfect, nor is the original t-minus-ten mark).


Previous discussion:
https://groups.google.com/d/topic/lojban-beginners/sWzqifBPUTU/discussion

Comment #4: Re: Issues
Curtis W Franks (Mon Jan 2 18:24:45 2017)

krtisfranks wrote:
> I think that there really are two words here.
>
> The first is "cardinality", which we already have. It is simple "x1 is
the
> number of elements in/cardinality of set x2". This uses on kancu2 and
> kancu3 (antirespectively). This requires no counter (person doing the
> counting) and is independent of the method used to count.
>
> The second word is something along the lines of "enumerate", "tabulate",
> "tally", or "count up". This is a task performed by someone (a counter)
and
> depends on the method. I personally think that it would be fine to
> straight-up delete kancu3 for this purpose, but perhaps we should just
> retool it (I am not sure how, though). Instead of trying to figure out
the
> cardinality of a set (kancu2), it would just be producing a running tally

> of objects/divisions/units (kancu2'). In this way, it is not actually
tied
> to the grand total, only what has thus far been counted.

Maybe this is a good option:

The cardinality of a set is equal to the cardinality of another set, by
definition, iff there exists a bijection between the sets. A set A is
called "countable" iff there exists a (possibly improper) subset of the set
of natural numbers B such that there exists a bijection between A and B. If
a set A is finite (therefore also countable), then its cardinality is the
nonnegative integer n such that there is a bijection between A and
ci'ai'u(n); A is countable and infinite iff its cardinality is
aleph-null.

The first word which I described would, for countable A, produce the n so
described (or, iff appropriate, aleph-null), regardless of which bijection
is used in order to relate A to the other set.

Note that, if there were a counter, then the wrong n may be produced by a
human method of counting (attempting but failing to produce a correct
bijection). This does not change the cardinality of the set, it just means
that the claim is false. For example, one can count by threes and come to
the conclusion that there were six Beatles, but that would not make them
correct. (In the current definition of kancu, they cannot possibly be
incorrect because their method of counting allows for them to come to
whichever conclusion they like.)

I offer a third possibility in replacing kancu now. This possibility does
not have a counter terbri (so it is like the word for cardinality in this
way) but it also does not have a terbri for the number at which the
counting would arrive (so it is like the second word which I described in
my first comment in this thread, which emphasizes the ongoing process of
tallying). This word merely describes /which/ bijection or injection, in
particular (of all of the possibilities), is being used/has been selected
in order to attempt to enumerate (some subset of) the set, where the
function maps from the set being counted to a subset of the natural numbers
united with the singleton of 0. In fact, in order to allow for joke
counting, repetition, or unforeseen uses, the function need not even be
injective nor mapping to N; it just needs to exist/be well-defined and map
to the set of extended real numbers (not even positive finite ones). Note
that, in partovular, ci'ai'u is not necessarily involved and that
ordering the range of the function is not necessary.

Comment #5: Re: Issues
Curtis W Franks (Tue Jan 3 00:33:39 2017)

krtisfranks wrote:
> The second word is something along the lines of "enumerate", "tabulate",
> "tally", or "count up". This is a task performed by someone (a counter)
and
> depends on the method.

Maybe the best way to describe this meaning is the idea that the counter
lists numbers sequentially (in order) (with a temporal or spatial delay
between each entry in the ordered list).

Changing the structure of the word somewhat, this would just require the
input of an ordered list, a description of what constitutes the start (if
counting eggs, which is the first one? if counting down seconds, what marks
when the countdown begins?), and what must happen in order to proceed from
one item in the list to the next one (pointing at a different egg, one
second passing, etc.). There would be no terbri for counting units/steps
(current kancu4), as this would just be derived information from the list
(and the counting unit would fluctuate/be variable as desired by the
counter).

Aside: That last point is important too. kancu is broken because it
cannot handle the counter adjusting the counting unit. Even if it could
handle the meaning "count( )down", and I do not think that it can, the unit
between numbers must be the same. That means that the events in that one
scene from /Harry Potter and the Prisoner of Azkaban/ movie from 2004,
which involves Dre Head counting down by varied units, cannot be described
by kancu under my current interpretation (that kancu4 must be a
constant).

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