BPFK Section: Inexact Numbers

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This page is imported from version 29 of the page BPFK Section: Inexact Numbers from the lojban Tiki.

Proposed definitions

su'o (PA4)

Proposed Definition

At least (one). Some.

See Also

  • {su'e}
  • {za'u}

Proposed Keywords

  • at least

Usage Examples

so'e lo ponjo jugle'u cu lerfu fi su'o re lo se bacru
Most Japanese kanji have at least two pronunciations.


su'e (PA4)

Proposed Definition

At most (one).

See Also

  • {su'o}
  • {me'i}

Proposed Keywords

  • at most

Usage Examples

la cibyska cu se kelci su'e bi remna
Tricolor is played by at most eight people.


za'u (PA3)

Proposed Definition

More than (one).

See Also

  • {me'i}
  • {su'o}
  • {dubmau}

Proposed Keywords

  • more than

Usage Examples

lo mi dalpe'o cu za'u mei
My pets are more than one.
za'u ci da cinri mi
There are more than three things that interest me.
ko za'u re'u troci
Try again!


me'i (PA3)

Proposed Definition

Less than (all). Not all.

See Also

  • {za'u}
  • {su'e}
  • {dubme'a}

Proposed Keywords

less than

Usage Examples

me'i gerku cu klama lo cevzda
Not all dogs go to heaven.


ji'i (PA4)

Proposed Definition

Approximately.

See Also

Proposed Keywords

  • approximately

Usage Examples

ji'i xa pi xa gigdo be lo remna cu xabju la terdi
Approximately 6.6 billion humans inhabit the Earth.


ro (PA4)

Proposed Definition

Each. All. Every.

See Also

  • {no}

Proposed Keywords

  • all
  • each
  • every

Usage Examples

lo srasu ro roi ri'ozma ze'o lo bitmu
The grass is always greener on the other side of the fence.


da'a (PA4)

Proposed Definition

All except (one).

See Also

  • {ro}

Proposed Keywords

  • all except

Usage Examples

da'a drata cu ci pa mei
All but one of the others are thirty-one-somes.


so'a (PA4)

Proposed Definition

Almost all. All but a few.

See Also

  • {so'u}

Proposed Keywords

  • almost all

Usage Examples

do so'a roi lerci
You're almost always late.


so'e (PA4)

Proposed Definition

Most. All but a significant number.

See Also

Proposed Keywords

  • most

Usage Examples

ta so'e mei
That's most of them.


so'i (PA4)

Proposed Definition

Many. A large number.

See Also

Proposed Keywords

  • many

Usage Examples

mi ba'o cilre so'i da lo xirma lo vi cukta
I have learned a lot about horses from this book.


so'o (PA4)

Proposed Definition

Several. A significant number.

See Also

Proposed Keywords

  • several

Usage Examples

so'o lo pendo be mi cu simlu lo ka jinvi lo du'u xamgu sidbo
Several of my friends seem to think it's a good idea.


so'u (PA4)

Proposed Definition

A few. A small number.

See Also

  • {so'a}

Proposed Keywords

  • a few

Usage Examples

mi stali lo darno ze'a lo masti be li so'u
I stayed away for a few months.


no'o (PA5)

Proposed Definition

A usual number. The expected number.

See Also

  • {xo'e}
  • {zu'i}

Proposed Keywords

  • usual number

Usage Examples

ba za lo mentu be li no'o mi co'a sipna
After the usual number of minutes, I fall asleep.


rau (PA4)

Proposed Definition

Enough. The right number.

See Also

  • {mo'a}
  • {du'e}

Proposed Keywords

  • enough

Usage Examples

xu do pu snada lo nu cpacu lo rau kelci
Did you manage to get enough players?


du'e (PA4)

Proposed Definition

Too many. More than the right number.

See Also

  • {mo'a}
  • {rau}

Proposed Keywords

  • too many

Usage Examples

du'e cuntu ka'e fliba
Too many things could go wrong.


mo'a (PA4)

Proposed Definition

Too few. Less than the right number.

See Also

  • {du'e}
  • {rau}

Proposed Keywords

  • too few

Usage Examples

mi'a mo'a roi casnu lo ckape
We discussed the dangers too few times.


Formal definitions

su'o PA vei na'u zmadu ja dunli PA
su'e PA vei na'u mleca ja dunli PA
za'u PA vei na'u zmadu PA
me'i PA vei na'u mleca PA
ji'i PA vei na'u jibni PA
da'a PA vei na'u se sumji be lo mulno PA
ro vei ni'e mulno
so'a vei ni'e muljbi
so'e vei ni'e xabmau
so'i vei ni'e mutce
so'o vei ni'e milxe
so'u vei ni'e toltce
rau vei ni'e drani
du'e vei ni'e dukse
mo'a vei ni'e toldu'e
no'o vei ni'e co'e

Notes

{dubdu'i}, {dubmau}, {dubme'a}, {dubnalmau} and {dubnalme'a} are probably more suitable predicates for dealing with number comparisons.


Quantifiers

definite :: no pa re ci vo mu xa ze bi ... da'aci da'are da'apa ro::
scalar ::no [ so'u ] [ so'o ] [ so'i ] [ so'e ] [ so'a ] ro::
generic ::no [ no'o ] ro::
subjective :: [ mo'a ] [ rau ] [ du'e ]::
ranges
su'o PA ::.......................... [PA ............................]::
za'u PA ::.......................... PA [............................]::
su'e PA ::[......................... PA] .............................::
me'i PA ::[.........................] PA .............................::
ji'i PA ::................... [...... PA ......] ........................::
da'a
da'a da'a PA PA
da'a ro no
da'a so'a so'u
da'a so'e so'o
da'a so'i so'i
da'a so'o so'e
da'a so'u so'a
da'a no ro
da'a rau rau
da'a du'e mo'a
da'a mo'a du'e
da'a no'o no'o
da'a su'o PA su'e da'a PA
da'a su'e PA su'o da'a PA
da'a za'u PA me'i da'a PA
da'a me'i PA za'u da'a PA
da'a ji'i PA ji'i da'a PA


Definitions in terms of su'o:
su'o N+1 da zo'u da broda su'o da su'o N de zo'u ge da na du de gi da .e de broda
za'u N da su'o N+1 da
su'e N da naku su'o N+1 da
me'i N da naku su'o N da
N da su'o N da .enai su'o N+1 da
da'a PA da PA da naku
In particular:
no da me'ipa da = naku su'o da
ro da da'ano da = no da naku = naku su'o da naku
With restricted da (i.e. da poi broda):
su'o da poi broda cu brode su'o da zo'u da broda gi'e brode
su'o N da poi broda cu brode su'o N da zo'u da broda gi'e brode
za'u N da poi broda cu brode za'u N da zo'u da broda gi'e brode
su'e N da poi broda cu brode su'e N da zo'u da broda gi'e brode
me'i N da poi broda cu brode me'i N da zo'u da broda gi'e brode
N da poi broda cu brode N da zo'u da broda gi'e brode
da'a Q da poi broda cu brode da'a Q da zo'u da broda nagi'a brode


Internal grammar of quantifiers

quantifier proportional / fractional
fractional [prefix] pi (indefinite / definite / prefix)
proportional simple & simple [fi'u (ro & definite) / ce'i]
simple prefix & (indefinite / definite)
prefix da'a & (su'o / su'e / me'i / za'u / ji'i) & da'a
indefinite so'u / so'o / so'i / so'e / so'a / ro / mo'a / rau / du'e / no'o
definite (no / pa / re / ci / vo / mu / xa / ze / bi / so / ki'o) ...

[ ] indicates the enclosed element is optional ... indicates the preceding element may appear one or more times / indicates either the preceding or the following element may appear & indicates the preceding, the following or both elements may appear

Defaults for bare prefix

When a prefix is not followed by a definite or indefinite, a default value is understood: the default is pa for su'o, su'e, za'u and da'a; ro for me'i; and a vague number (perhaps no'o) for ji'i.

Two adjacent simple quantifiers

  • Two adjacent simple quantifiers are interpreted, when possible, as if joined with .e:
 ro ci broda 
 all three brodas, all brodas and three brodas.

 rau su'o mu broda
 enough at least five brodas, enough brodas and at least five brodas.

 su'o ci su'e bi broda
 at least three at most eight brodas
 at least three brodas and at most eight brodas
 between three and eight brodas (inclusive)
  • Two adjacent simple quantifiers are interpreted, when joining them with .e would give a contradiction, as if joined with .a:
 me'i ci za'u ci broda
 less than three more than three brodas
 less than three brodas or more than three brodas
 i.e. other than three brodas

 mo'a du'e broda
 too few too many brodas
 too few brodas or too many brodas
 the wrong number of brodas


Proportional quantifiers

re fi'u ci broda Two out of every three brodas. Two thirds of brodas.

za'u vo fi'u mu broda More than four out of every five brodas. More than four fifths of brodas.

du'a fi'u ro muno broda Too many out of all 50 broda. Too many broda, of which there are 50 in all.

  • ce'i is equivalent to fi'u panono:
za'u munoce'i broda
More than half of all brodas.

da'a cirepimu ce'i broda
All but 32.5% of brodas.

Fractional quantifiers

piPA sumti lo piPA si'e be sumti

When a sumti has a single referent (which may be a simple individual, a group, a set, etc.) then a fractional quantifier refers to a corresponding fraction of the referent. In particular, a fraction of a group or a set is a subgroup or subset whose cardinality is the corresponding fraction of the cardinality of the whole.

When a sumti has more than one referent (e.g. le ci plise) then a fractional quantifier refers to a fraction of one (which one is not specified) of the referents. Then pimu le ci plise is "half of one of the three apples. Then more generally we can define:

piPA sumti lo piPA si'e be pa me sumti

which will also cover the case of a single referent.

We may then generalize to things like repimu le ci plise for "two and a half of the three apples".


Issues

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