Re: Types of numerals; bases in natlangs.

Hi!

John Vertical <johnvertical@...> writes:
> Henrik Theiling wrote:
>...
> >    Number ::= Exponent Base Sequence_of_digits
> >
> >Where Exponent is itself a Number. Base is the base word, (often
> >enough, this is therefore '10').  Any of the three Exponent, Base and
> >Sequence_of_digits may be empty if trivial, but at least one of them
> >must be given.
>
> >To understand the system:
>
> >   20 = kjox kul          = '10 2'
> >   12 = kjox ling kul     = '10 1 2'
> >
> >  100 = kul kjox          = '2 10'
> >  300 = kul kjox hen      = '2 10 3'
> >  120 = kul kjox ling kul = '2 12 1 2'
>
> So Base defaults to 10, Digits defaults to 1 followed by x zeroes, and
> Exponent defaults to the number of digits
No, the exponent defaults to one.

Further, if there is more than one digit, the base must be specified
even if it is one.

> (except a leading 1 does not count)? So then, 1.2 would be "ling
> kjox ling kul", right?
No, that's 12.  With 'tjen' being 'zero', 'tjen kjok ling kul' means
'1.2'.

> >And now:
> >
> >  3*10^20    = kjox kul kjox hen    = '10 2 10 3'
> >  10^300     = kul kjox hen kjox    = '2 10 3 10'
> >
> >Is this understandable?
>
> Definitely ambiguous.
No, definitely unambiguous. :-)

But maybe to accept this I should have mentioned that the above is the
short form of numbers in environments where the base is agreed on.
Further, the base is constant throughout the number by default unless
stated otherwise.  So 'kjox' is more the exponent marker in base 10
environments.

If the base is not agreed on, the first used base must be in the long
form, using the verb 'to take the power of' explicitly.  This verb is
'il':

    kul il kjok == 10^2 = 100

For long numbers with many zeros in the sequence of digits, there is
another verb 'wng' which means 'to add':

    hen il kjok wng ling = 1001

('wng' cannot be used in exponents.)

Further, there's a word for 'minus' to specify negative numbers and
fractions.

>...  Even if you disallow digits if the base is something else than
>10, you still get cases like "kjox kul kjox hen" having an
>alternative analysis as "30^20".
Because the exponent is agreed on when using the short number form,
'kjox kul kjox hen' this can only mean:

  3*10^20

> OTOH, if Base must always be 10, I don't see why it needs to be
> specified at all;
To mark the border between exponent and sequence of digits.

> you can do with just a marker for "number ends".
It basically functions just like that for the exponent.

>...
> Are there any other instances where Base can be omitted than the
> natural numbers 0 thru 9? Will "hen kul" mean anything??
Not officially; only in base 3.  But in very casual speech, you're
likely to hear it anyway in base ten environments.  Pedants will then
immediately ask for the order of magnitude, though, or will assume
base three. :-)

**Henrik

--
Relay 13 is forthcoming:
http://www.conlang.info/relay/relay13.html

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