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 > straightup 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 alephnull.
The first word which I described would, for countable A, produce the n so described (or, iff appropriate, alephnull), 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 welldefined 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.
