Subject: Numbers

From: "Jorge Llambias" <[email-masked]>
Date: Tue, 13 Mar 2001 20:47:28

Here is an informal grammar of numbers. I am not even
suggesting that this should be part of the formal grammar,
it is just an exercise to sort out which combinations
of PA make sense and which don't. I can make some sort of
sense of all combinations generated by this grammar. As
for those not generated by it, maybe some meaning could
eventually be found for them, but there is nothing as
yet defined as far as I can tell.

<pre-sign> = (ji'i|su'e|su'o|me'i|za'u)...
<sign> = ma'u|ni'u
<digit> = no|pa|re|ci|vo|mu|xa|ze|bi|so|dau|fei|gai|jau|rei|vai|ki'o|xo
<indef> = ro|so'a|so'e|so'i|so'o|so'u|su'o|da'a|no'o|rau|du'e|mo'a
<bare> = [<digit>...][pi [<digit>...][ra'e <digit>...]]|[pi] <indef>
<real> = [<pre-sign>][<sign>][<bare>|ci'i|pai|te'o][ce'i]
<fraction> = [<real>][fi'u <real>]
<complex> = [<fraction>][ka'o <fraction>] | tu'o
<n-tuple> = [<complex>][pi'e <complex>]...

Notes:
1- I didn't put the indefinites at the same level as the digits,
because it doesn't really make sense to me for {so'a} to stand
for 8 or 9, {so'e} for 6 or 7, etc. To me they are always full
numbers, not positional digits.
2- I allowed {ce'i} in a couple of weird places, for example you
could say {muce'ifi'ucice'i}, 5%/3%, which does not have a very
obvious meaning, but to restrict {ce'i} more would have complicated
the grammar a lot and it didn't seem justified.
3- I chose to make {fi'u} more close binding than {ka'o}. Either
choice was possible. So {cika'ovofi'umu} is 3+(4/5)i and not
(3+4i)/5.
4- I didn't allow double fractions, so that 3/4/5 is neither
(3/4)/5 nor 3/(4/5), it is simply not meaningful in my scheme.
5- I allowed fractions such as 3.5/2.7, why not?
6- Probably {ji'i} needs more work, but I didn't want it as a
positional digit.
7- I left {xo} as a positional digit, but I have my doubts about it.

Comments welcome!

co'o mi'e xorxes

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