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lojbau mekso: Mathematical Expressions in Lojban
The Lojban Reference Grammar |
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The following cmavo are discussed in this section:
mei MOI cardinal selbri
moi MOI ordinal selbri
si'e MOI portion selbri
cu'o MOI probability selbri
va'e MOI scale selbri
me ME make sumti into selbri
me'u MEhU terminator for ME
Lojban possesses a special category of selbri which are based
on mekso. The simplest kind of such selbri are made by
suffixing a member of selma'o MOI to a number. There are four
members of MOI, each of which serves to create number-based
selbri with specific place structures.
``-mei'' creates cardinal selbri. The basic place structure is:
Some examples:
11.1) lei mi ratcu cu cimei
those-I-describe-as-the-mass-of my rats are-a-threesome.
My rats are three.
I have three rats.
Here, the mass of my rats is said to have three components; that is, I have three rats.
Another example, with one element this time:
11.2) mi poi pamei cu cusku dei
I who am-an-individual express this-sentence.
In Example 11.2, ``mi'' refers to a mass, ``the mass consisting of me''. Personal pronouns are vague between masses, sets, and individuals.
However, when the number expressed before ``-mei'' is an objective indefinite number of the kind explained in Section 8, a slightly different place structure is required:
An example:
11.3) lei ratcu poi zvati le panka cu so'umei
fo lo'i ratcu
the-mass-of rats which are-in the park are a-fewsome
with-respect-to the-set-of rats.
The rats in the park are a small number
of all the rats there are.
In Example 11.3, the x2 and x3 places are
vacant, and the x4 place is filled by ``lo'i ratcu'', which
(because no quantifiers are explicitly given) means ``the whole
of the set of all those things which are rats'', or simply
``the set of all rats.''
11.4) le'i ratcu poi zvati le panka cu se so'imei
The-set-of rats which-are in the park is-a manysome.
There are many rats in the park.
In Example 11.4, the conversion cmavo ``se'' swaps the x1 and the x2 places, so that the new x1 is the set. The x4 set is unspecified, so the implication is that the rats are ``many'' with respect to some unspecified comparison set.
More explanations about the interrelationship of sets, masses, and individuals can be found in Chapter 6.
``-moi'' creates ordinal selbri. The place structure is:
Some examples:
11.5) ti pamoi le'i mi ratcu
This-one is the first-of the rats associated-with me.
This is my first rat.
11.6) ta romoi le'i mi ratcu
That is-the-allth-of the rats associated-with me.
That is my last rat.
11.7) mi raumoi le velskina porsi
I am-enough-th-in the movie-audience sequence
I am enough-th in the movie line.
Example 11.7 means, in the appropriate
context, that my position in line is sufficiently far to the
front that I will get a seat for the movie.
``-si'e'' creates portion selbri. The place structure is:
Some examples:
11.8) levi sanmi cu fi'ucisi'e lei mi djedi cidja
This-here meal is-a-slash-three-portion-of my day-food.
This meal is one-third of my daily food.
``-cu'o'' creates probability selbri. The place structure is:
11.9) le nu lo sicni cu sedja'o cu pimucu'o
The event of a coin being a head-displayer
has probability .5.
``-va'e'' creates a scale selbri. The place structure is:
11.10) le vi rozgu cu sofi'upanova'e xunre
This rose is 8/10-scale red
This rose is 8 out of 10 on the scale of redness.
This rose is very red.
When the quantifier preceding any MOI cmavo includes the
subjective numbers ``rau'', ``du'e'', or ``mo'a'' (enough, too
many, too few) then an additional place is added for ``by
standard''. For example:
11.11) le ratcu poi zvati le panka cu du'emei fo mi
The rats which-are in the park are too-many
by-standard me.
There are too many rats in the park for me.
The extra place (which for ``-mei'' is the x4 place labeled by
``fo'') is provided rather than using a BAI tag such as
``ma'i'' because a specification of the standard for judgment
is essential to the meaning of subjective words like
``enough''.
This place is not normally explicit when using one of the subjective numbers directly as a number. Therefore, ``du'e ratcu'' means ``too many rats'' without specifying any standard.
It is also grammatical to substitute a lerfu string for a number:
11.12) ta ny.moi le'i mi ratcu
that is-nth-of the-set-of my rats
That is my nth rat.
More complex mekso cannot be placed directly in front of MOI,
due to the resulting grammatical ambiguities. Instead, a
somewhat artificial form of expression is required.
The cmavo ``me'' (of selma'o ME) has the function of making a sumti into a selbri. It is often used to make a name into a predicate:
11.13) ti me la nu,IORK. [me'u]
this-here pertains-to what-I-call ``New York''.
This is New York (or is New York-related).
A whole ``me'' construction can have a member of MOI added to
the end to create a complex mekso selbri:
11.14) ta me li ny. su'i pa me'u moi le'i mi ratcu
that is the-number n plus one-th-of the-set-of my rats.
That is my (n+1)-th rat.
Here the mekso ``ny. su'i pa'' is made into a sumti (with ``li'') and then changed into a mekso selbri with ``me'' and ``me'u moi''. The elidable terminator ``me'u'' is required here in order to keep the ``pa'' and the ``moi'' separate; otherwise, the parser will combine them into the compound ``pamoi'' and reject the sentence as ungrammatical.
It is perfectly possible to use non-numerical sumti after ``me'' and before a member of MOI, producing strange results indeed:
11.15) le nu mi nolraitru
cu me le'e snime bolci
be vi la xel. cu'o
The event-of me being-a-nobly-superlative-ruler
has-the-stereotypical snow type-of-ball
at Hell probability.
I have a snowball's chance in Hell of being king.
Note: the elidable terminator ``boi'' is not used between a
number and a member of MOI. As a result, the ``me'u'' in Example 11.14 could also be replaced by a
``boi'', which would serve the same function of preventing the
``pa'' and ``moi'' from joining into a compound.
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Previous
Non-decimal and compound bases |
lojbau mekso: Mathematical Expressions in Lojban
The Lojban Reference Grammar |
Next
Number questions |