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Discussion of "ci'i"

Comment #1: Complex infinity, etc.
Curtis W Franks (Fri Jun 2 22:59:12 2017)

First, this word should have no implicit signum. It should allow for
reference to anything which is in any way infinite, unless restricted by
context. If you want positive infinity, then use "ma'uci'i". If you want
negative infinity, then use "ni'uci'i". Some extensions of the reals do
not distinguish these, but that is neither here nor there. I personally do
not even think that it has to be in the extended reals. It could be complex
infinity. It could be a transfinite cardinal, or a transfinite ordinal, or
something else. It just has to somehow encapsulate the most generic sense
of infinity.

Second, I am not sure how to specify exactly "complex infinity". Naively, I
would recommend "ci'ika'o'ei", but we have a conflict there. If
"ka'o'ei" belongs to PA, then the definition of "ci'i" does not allow
it to be meaningfully followed by anything other than a nonnegative real
number or a transfinite number. There is no such thing as aleph-(1+2i),
where i is the imaginary unit, for example. Even if it were allowed for
this purpose, it not clear to me why one word should override the other in
precedence. It gets worse if we say "ci'i pa ka'o'ei" - does the "pa" go
with "ci'i" or "ka'o'ei", or are these each digits in some weird base?
Returning to "ci'ika'o'ei" (no inserted "pa"), if "ci'i" takes precedence,
then what numbers implicitly fill the left and right sides of "ka'o'ei".
If "ka'o'ei" is reclassified into/as VUhU (as I recommend), then we have a
compound cmavo of two different selma'o, so I am not sure how to classify
the result, but it would at least be interpreted correctly as referring to
complex infinity.

Third, even without that hiccup, I think that we really should consider
diversifying our vocabulary so that transfinite cardinals get introduced
with their own word. I do not see why they should be preferred over
ordinals or beth numbers, etc. And any such transfinite thing should,
perhaps, be put in VUhU too. Otherwise, it temporarily breaks the reading
of the digit string as belonging to a base (such as the contextless default
of decimal). Even just "ci'ino" in our current definition (not as VUhU+PA)
should refer to infty*(10^1) + 0*(10^0) = infty, where "10" refers to the
base (contextless default: decimal).

Comment #2: Re: Complex infinity, etc.
Curtis W Franks (Fri Jun 2 23:01:56 2017)

krtisfranks wrote:
> And any such transfinite thing should,
> perhaps, be put in VUhU too. Otherwise, it temporarily breaks the reading

> of the digit string as belonging to a base (such as the contextless
default
> of decimal). Even just "ci'ino" in our current definition (not as
VUhU+PA)
> should refer to infty*(10^1) + 0*(10^0) = infty, where "10" refers to the

> base (contextless default: decimal).

See also: "ci'i'e", "ci'i'o", "ci'i'oi".

The recommendation of putting "ci'i" in VUhU applies to them as well.

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