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[Wikineurotic] Wiki page BPFK Section: Inexact Numbers changed by Ilmen
The page BPFK Section: Inexact Numbers was changed by Ilmen at 16:26 CEST
Comment: Adding a note.
You can view the page by following this link:
http://www.lojban.org/tiki/BPFK%20Section%3A%20Inexact%20Numbers
You can view a diff back to the previous version by following this link:
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- !!Formal definitions
+ !! Formal definitions
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no'o | vei ni'e co'e
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+
+ !! Notes
+ {dubmau}, {dubme'a}, {dubnalmau} and {dubnalme'a} are probably more suitable predicates for dealing with number comparisons.
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The new page content follows below.
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!Proposed definitions
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!! 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.''
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!! 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.''
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!! za'u (PA3)
!!! Proposed Definition
More than (one).
!!! See Also
* {me'i}
* {su'o}
!!! 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!''
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!! me'i (PA3)
!!! Proposed Definition
Less than (all). Not all.
!!! See Also
* {za'u}
* {su'e}
!!! Proposed Keywords
less than
!!! Usage Examples
;me'i gerku cu klama lo cevzda:''Not all dogs go to heaven.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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.''
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!! 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?''
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!! 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.''
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!! 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.''
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!! 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
{dubmau}, {dubme'a}, {dubnalmau} and {dubnalme'a} are probably more suitable predicates for dealing with number comparisons.
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!!Quantifiers
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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
||
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!!Internal grammar of quantifiers
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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".
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!! Issues
* [http://groups.google.com/group/lojban/browse_thread/thread/7faee6194afce4ec|The only link I ( mi'e la .lindar. ) will provide regarding "existential importing" regarding 'ro'.]
* [https://groups.google.com/group/lojban/tree/browse_frm/month/2005-08/caad646bf14f367f?rnum=21&_done=%2Fgroup%2Flojban%2Fbrowse_frm%2Fmonth%2F2005-08%3F#doc_d8d0beca5407594b|ji'i ?]
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