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[bpfk] dag-cll git updates for Tue Nov 2 23:21:01 EDT 2010
commit 67ca2cd4034a978466ed3edf306ff5b5559f049f
Author: Robin Lee Powell <rlpowell@digitalkingdom.org>
Date: Tue Nov 2 19:44:34 2010 -0700
Various updates to be more in line with the red book, although
section 22 had a bunch of "li" added to make it parse.
diff --git a/18/10/index.html b/18/10/index.html
index e5d4941..297045f 100644
--- a/18/10/index.html
+++ b/18/10/index.html
@@ -51,21 +51,21 @@ Here, the final “pa no” is assumed to be base 10, as usual; so is the base s
<a id="e3" name="e3">10.3)</a> li jaureivai ju'u paxa du li cimuxaze
The-number DEF base 16 equals the-number 3567.
</pre>
Note the pattern in the cmavo: the diphthongs “au”, “ei”, “ai” are used twice in the same order. The digits for A to D use consonants different from those used in the decimal digit cmavo; E and F unfortunately overlap 2 and 4 — there was simply not enough available cmavo space to make a full differentiation possible. The cmavo are also in alphabetical order.
<p>The base point “pi” is used in non-decimal bases just as in base 10:</p>
<pre>
<a id="e4" name="e4">10.4)</a> li vai pi bi ju'u paxa du li pamu pi mu
The-number F.8 base 16 equals the-number 15.5.
</pre>
-Since “ju'u” is an operator of selma'o VUhU, it is grammatical to use any operand as the left argument. Semantically, however, it is undefined to use anything but a numeral string on the left. The reason to make “ju'u” an operator is to allow reference to a base which is not a constant.
+Since “ju'u” is an operator of selma'o VUhU, it is grammatical to use any operand as the left argument. Semantically, however, it is undefined to use anything but a numeral string on the left. The reason for making “ju'u” an operator is to allow reference to a base which is not a constant.
<p>There are some numerical values that require a “base” that varies from digit to digit. For example, times represented in hours, minutes, and seconds have, in effect, three “digits”: the first is base 24, the second and third are base 60. To express such numbers, the compound base separator “pi'e” is used:</p>
<pre>
<a id="e5" name="e5">10.5)</a> ci pi'e rere pi'e vono
3:22:40
</pre>
Each digit sequence separated by instances of “pi'e” is expressed in decimal notation, but the number as a whole is not decimal and can only be added and subtracted by special rules:
<pre>
<a id="e6" name="e6">10.6)</a> li ci pi'e rere pi'e vono su'i pi'e ci pi'e cici du li ci pi'e rexa pi'e paci
The-number 3:22:40 plus :3:33 equals the-number 3:26:13.
3:22:40 + 0:3:33 = 3:26:13
@@ -80,21 +80,21 @@ Of course, only context tells you that the first part of the numbers in <a href=
<pre>
<a id="e8" name="e8">10.8)</a> pano ju'u reno
the-digit-10 base 20
</pre>
which is equal to ten, and:
<pre>
<a id="e9" name="e9">10.9)</a> pa pi'e no ju'u reno
1;0 base 20
</pre>
which is equal to twenty.
-<p>Both “pi” and “pi'e” can be used to express large-base decimal fractions:</p>
+<p>Both “pi” and “pi'e” can be used to express large-base fractions:</p>
<pre>
<a id="e10" name="e10">10.10)</a> li pa pi'e vo pi ze ju'u reno du li re vo pi ci mu
The-number 1;4.7 base 20 equals the-number 24.35.
</pre>
“pi'e” is also used where the base of each digit is vague, as in the numbering of the examples in this chapter:
<pre>
<a id="e11" name="e11">10.11)</a> dei jufra panopi'epapamoi
This-utterance is-a-sentence-type-of 10;11th-thing.
This is Sentence 10.11.
</pre>
diff --git a/18/11/index.html b/18/11/index.html
index f2b3092..71762d7 100644
--- a/18/11/index.html
+++ b/18/11/index.html
@@ -111,58 +111,58 @@ Some examples:
</pre>
The number must be between 0 and 1 inclusive. For example:
<pre>
<a id="e9" name="e9">11.9)</a> le nu lo sicni cu sedja'o cu pimucu'o
The event of a coin being a head-displayer has probability .5.
</pre>
<p>The cmavo “va'e” creates a scale selbri. The place structure is:</p>
<pre>
x1 is at scale position (n) on the scale x2
</pre>
-If the scale is granular rather than continuous, a form like “cifi'uxa” (3/6) may be used; in this case, 3/6 is not the same as 1/2. Here is an example:
+If the scale is granular rather than continuous, a form like “cifi'uxa” (3/6) may be used; in this case, 3/6 is not the same as 1/2, because the third position on a scale of six positions is not the same as the first position on a scale of two positions. Here is an example:
<pre>
<a id="e10" name="e10">11.10)</a> le vi rozgu cu sofi'upanova'e xunre
This rose is 9/10-scale red.
This rose is 9 out of 10 on the scale of redness.
This rose is very red.
</pre>
<p>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:</p>
<pre>
-<a id="e11" name="e11">11.11)</a> le ratcu poi zvati le panka cu du'emei fo mi
- The rats which-are in the park are too-many by-standard me.
+<a id="e11" name="e11">11.11)</a> lei ratcu poi zvati le panka cu du'emei fo mi
+ The-mass-of rats which-are in the park are too-many by-standard me.
There are too many rats in the park for me.
</pre>
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”.
<p>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.</p>
<p>It is also grammatical to substitute a lerfu string for a number:</p>
<pre>
<a id="e12" name="e12">11.12)</a> ta ny.moi le'i mi ratcu
That is-nth-of the-set-of my rats.
That is my nth rat.
</pre>
<p>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.</p>
-<p>The cmavo “me” (of selma'o ME) has the function of making a sumti into a selbri. A whole “me” construction can have a member of MOI added to the end to create a complex mekso bridi:</p>
+<p>The cmavo “me” (of selma'o ME) has the function of making a sumti into a selbri. A whole “me” construction can have a member of MOI added to the end to create a complex mekso selbri:</p>
<pre>
<a id="e13" name="e13">11.13)</a> 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.
</pre>
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.
<p>It is perfectly possible to use non-numerical sumti after “me” and before a member of MOI, producing strange results indeed:</p>
<pre>
-<a id="e15" name="e15">11.15)</a> le nu mi nolraitru
+<a id="e14" name="e14">11.14)</a> 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.
</pre>
-Note: the elidable terminator “boi” is not used between a number and a member of MOI. As a result, the “me'u” in <a href="../11/#e14">Example 11.14</a> could also be replaced by a “boi”, which would serve the same function of preventing the “pa” and “moi” from joining into a compound.
+Note: the elidable terminator “boi” is not used between a number and a member of MOI. As a result, the “me'u” in <a href="../11/#e13">Example 11.13</a> could also be replaced by a “boi”, which would serve the same function of preventing the “pa” and “moi” from joining into a compound.
<hr />
<div class="nav">
<div class="nav-prev">
<div class="nav-section-link-prev"><a href="../../18/10/">Previous</a></div>
<div class="nav-section-name">Non-decimal and compound bases</div>
</div>
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<div class="nav-section-name">Number questions</div>
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diff --git a/18/14/index.html b/18/14/index.html
index cbfd95e..5e29b08 100644
--- a/18/14/index.html
+++ b/18/14/index.html
@@ -49,21 +49,21 @@ The “tu'o” fulfills the grammatical requirement for a left operand for the i
Why are the arguments to “gei” in reverse order from the conventional symbolic notation? So that “gei” can be used in forethought to allow easy specification of a large (or small) imprecise number:
<pre>
<a id="e3" name="e3">14.3)</a> gei reno
(scientific) two-zero
10<sup>20</sup>
</pre>
Note, however, that although 10 is far and away the most common exponent base, it is not the only possible one. The third operand of “gei”, therefore, is the base, with 10 as the default value. Most computers internally store so-called “floating-point” numbers using 2 as the exponent base. (This has nothing to do with the fact that computers also represent all integers in base 2; the IBM 360 series used an exponent base of 16 for floating point, although each component of the number was expressed in base 2.) Here is a computer floating-point number with a value of 40:
<pre>
<a id="e4" name="e4">14.4)</a> papano bi'eju'u re gei pipanopano bi'eju'u re ge'a re
(one-one-zero base 2) scientific (point-one-zero-one-zero base 2) with-base 2
- .1010<!--<sub>2</sub>--> × 2<sup>110<sub>2</sub></sup>
+ .1010<sub>2</sub> × 2<sup>110<sub>2</sub></sup>
</pre>
<hr />
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<div class="nav-section-name">Subscripts</div>
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<div class="nav-section-name">Vectors and matrices</div>
diff --git a/18/19/index.html b/18/19/index.html
index 06bcd91..8016189 100644
--- a/18/19/index.html
+++ b/18/19/index.html
@@ -83,21 +83,21 @@ where the “na'u nu'a” cancels out, leaving a truthful bridi
<a id="e9" name="e9">19.9)</a> romai
all-ly
lastly
<a id="e10" name="e10">19.10)</a> ny.mai
nth-ly
<a id="e11" name="e11">19.11)</a> pasomo'o
nineteenthly (higher order)
</pre>
-The difference between “mai” and “mo'o” is that “mo'o” enumerates larger subdivisions of a text. Each “mo'o” subdivision can then be divided into pieces and internally numbered with “mai”. If this chapter were translated into Lojban, it would number each section with “mo'o”. (See <a href="../../19/1/">Chapter 19</a> for more on these words.)
+The difference between “mai” and “mo'o” is that “mo'o” enumerates larger subdivisions of a text. Each “mo'o” subdivision can then be divided into pieces and internally numbered with “mai”. If this chapter were translated into Lojban, each section would be numbered with “mo'o”. (See <a href="../../19/1/">Chapter 19</a> for more on these words.)
<p>A numerical tense can be created by suffixing a digit string with “roi”. This usage generates tenses corresponding to English “once”, “twice”, and so on. This topic belongs to a detailed discussion of Lojban tenses, and is explained further in <a href="../../10/1/">Chapter 10</a>.</p>
<p>Note: the elidable terminator “boi” is not used between a number and a member of MAI or ROI.</p>
<hr />
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<div class="nav-section-name">Using Lojban resources within mekso</div>
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diff --git a/18/20/index.html b/18/20/index.html
index 8b3c38c..f7c1bcf 100644
--- a/18/20/index.html
+++ b/18/20/index.html
@@ -19,21 +19,21 @@
<div class="nav-section-name">Miscellany</div>
</div>
<div class="nav-title">
<div class="nav-title-title">lojbau mekso: Mathematical Expressions in Lojban</div>
<div class="nav-title-link"><a href="../../">The Lojban Reference Grammar</a></div>
</div>
</div>
<hr />
<h3>20. Explicit operator precedence</h3>
<p>As mentioned earlier, Lojban does provide a way for the precedences of operators to be explicitly declared, although current parsers do not understand these declarations.</p>
-<p>The declaration is made in the form of a metalinguistic comment using “ti'o”, a member of selma'o SEI. “sei”, the other member of SEI, is used to insert metalinguistic comments on a bridi which give information about the discourse which the bridi comprises. The format of a “ti'o” declaration has not been formally established, but presumably would take the form of mentioning a mekso operator and then giving it either an absolute numerical precedence on some established scale, or else specifying relative precedences between new operators and existing operators.</p>
+<p>The declaration is made in the form of a metalinguistic comment using “ti'o”, a member of selma'o SEI. “sei”, the other member of SEI, is used to insert metalinguistic comments on a bridi which give information about the discourse which the bridi comprises. The format of a “ti'o” declaration has not been formally established, but presumably would take the form of mentioning a mekso operator and then giving it either an absolute numerical precedence on some pre-established scale, or else specifying relative precedences between new operators and existing operators.</p>
<p>In future, we hope to create an improved machine parser that can understand declarations of the precedences of simple operators belonging to selma'o VUhU. Originally, all operators would have the same precedence. Declarations would have the effect of raising the specified cmavo of VUhU to higher precedence levels. Complex operators formed with “na'u”, “ni'e”, or “ma'o” would remain at the standard low precedence; declarations with respect to them are for future implementation efforts. It is probable that such a parser would have a set of “commonly assumed precedences” built into it (selectable by a special “ti'o” declaration) that would match mathematical intuition: times higher than plus, and so on.</p>
<hr />
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<div class="nav-section-name">Other uses of mekso</div>
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<div class="nav-section-name">Miscellany</div>
diff --git a/18/22/index.html b/18/22/index.html
index e52f590..ca783ea 100644
--- a/18/22/index.html
+++ b/18/22/index.html
@@ -20,39 +20,39 @@
</div>
<div class="nav-title">
<div class="nav-title-title">lojbau mekso: Mathematical Expressions in Lojban</div>
<div class="nav-title-link"><a href="../../">The Lojban Reference Grammar</a></div>
</div>
</div>
<hr />
<h3>22. Four score and seven: a mekso problem</h3>
<p>Abraham Lincoln’s Gettysburg Address begins with the words “Four score and seven years ago”. This section exhibits several different ways of saying the number “four score and seven”. (A “score”, for those not familiar with the term, is 20; it is analogous to a “dozen” for 12.) The trivial way:</p>
<pre>
-<a id="e1" name="e1">22.1)</a> bize
+<a id="e1" name="e1">22.1)</a> li bize
eight seven
87
</pre>
<a href="../22/#e1">Example 22.1</a> is mathematically correct, but sacrifices the spirit of the English words, which are intended to be complex and formal.
<pre>
-<a id="e2" name="e2">22.2)</a> vo pi'i reno su'i ze
+<a id="e2" name="e2">22.2)</a> li vo pi'i reno su'i ze
four times twenty plus seven
4 × 20 + 7
</pre>
<a href="../22/#e2">Example 22.2</a> is also mathematically correct, but still misses something. “Score” is not a word for 20 in the same way that “ten” is a word for 10: it contains the implication of 20 objects. The original may be taken as short for “Four score years and seven years ago”. Thinking of a score as a twentysome rather than as 20 leads to:
<pre>
-<a id="e3" name="e3">22.3)</a> mo'e voboi renomei su'i ze [DOES NOT PARSE]
+<a id="e3" name="e3">22.3)</a> li mo'e voboi renomei te'u su'i ze
the-number-of four twentysomes plus seven
</pre>
In <a href="../22/#e3">Example 22.3</a>, “voboi renomei” is a sumti signifying four things each of which are groups of twenty; the “mo'e” and “te'u” then make this sumti into a number in order to allow it to be the operand of “su'i”.
<p>Another approach is to think of “score” as setting a representation base. There are remnants of base-20 arithmetic in some languages, notably French, in which 87 is “quatre-vingt-sept”, literally “four-twenties-seven”. (This fact makes the Gettysburg Address hard to translate into French!) If “score” is the representation base, then we have:</p>
<pre>
-<a id="e4" name="e4">22.4)</a> vo pi'e ze ju'u reno
+<a id="e4" name="e4">22.4)</a> li vo pi'e ze ju'u reno
four ; seven base 20
47<sub>20</sub>
</pre>
Overall, <a href="../22/#e3">Example 22.3</a> probably captures the flavor of the English best. <a href="../22/#e1">Example 22.1</a> and <a href="../22/#e2">Example 22.2</a> are too simple, and <a href="../22/#e4">Example 22.4</a> is too tricky. Nevertheless, all four examples are good Lojban. Pedagogically, these examples illustrate the richness of lojbau mekso: anything that can be said at all, can probably be said in more than one way.
<hr />
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<div class="nav-section-name">Miscellany</div>
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diff --git a/18/3/index.html b/18/3/index.html
index ce65cf1..6064b87 100644
--- a/18/3/index.html
+++ b/18/3/index.html
@@ -82,21 +82,21 @@ Note that the “ra'e” marks unambiguously where the repeating portion “1428
1,023,004
</pre>
In the same way, “ki'o” can be used after “pi” to divide fractions into groups of three:
<pre>
<a id="e9" name="e9">3.9)</a> pi ki'o re re
point comma two two
.022
<a id="e10" name="e10">3.10)</a> pi pa ki'o pa re ki'o pa
point one comma one two comma one
- .101012001
+ .001012001
</pre>
<hr />
<div class="nav">
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<div class="nav-section-link-prev"><a href="../../18/2/">Previous</a></div>
<div class="nav-section-name">Lojban numbers</div>
</div>
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<div class="nav-section-name">Special numbers</div>
diff --git a/18/5/index.html b/18/5/index.html
index bc83bf4..2f70233 100644
--- a/18/5/index.html
+++ b/18/5/index.html
@@ -88,21 +88,21 @@ Is the Lojban version of <a href="../5/#e7">Example 5.7</a> true? No! “3 + 4
Here we calculate 3 + 4 first, giving 7, and then calculate 7 × 5 second, leading to the result 35. While possessing the advantage of simplicity, this result violates the design goal of matching the standards of mathematics. What can be done?
<p>There are three solutions, all of which will probably be used to some degree. The first solution is to ignore the problem. People will say “li ci su'i vo pi'i mu” and mean 23 by it, because the notion that multiplication takes precedence over addition is too deeply ingrained to be eradicated by Lojban parsing, which totally ignores semantics. This convention essentially allows semantics to dominate syntax in this one area.</p>
<p>(Why not hard-wire the precedences into the grammar, as is done in computer programming languages? Essentially because there are too many operators, known and unknown, with levels of precedence that vary according to usage. The programming language ’C’ has 13 levels of precedence, and its list of operators is not even extensible. For Lojban this approach is just not practical. In addition, hard-wired precedence could not be overridden in mathematical systems such as spreadsheets where the conventions are different.)</p>
<p>The second solution is to use explicit means to specify the precedence of operators. This approach is fully general, but clumsy, and will be explained in <a href="../20/">Section 20</a>.</p>
<p>The third solution is simple but not very general. When an operator is prefixed with the cmavo “bi'e” (of selma'o BIhE), it becomes automatically of higher precedence than other operators not so prefixed. Thus,</p>
<pre>
<a id="e9" name="e9">5.9)</a> li ci su'i vo bi'e pi'i mu du li reci
The-number three plus four-times-five equals the-number two-three.
3 + 4 × 5 = 23
</pre>
-is a truthful Lojban bridi. If more than one operator has a “bi'e” prefix, grouping is to the right; multiple “bi'e” prefixes on a single operator are not allowed.
+is a truthful Lojban bridi. If more than one operator has a “bi'e” prefix, grouping is from the right; multiple “bi'e” prefixes on a single operator are not allowed.
<p>In addition, of course, Lojban has the mathematical parentheses “vei” and “ve'o”, which can be used just like their written equivalents “(” and “)” to group expressions in any way desired:</p>
<pre>
<a id="e10" name="e10">5.10)</a> li vei ny. su'i pa ve'o pi'i vei ny. su'i pa [ve'o] du
li ny. [bi'e] te'a re su'i re bi'e pi'i ny. su'i pa
The-number (“n” plus one) times (“n” plus one)
equals the-number n-power-two plus two-times-“n” plus 1.
(n + 1)(n + 1) = n<sup>2</sup> + 2n + 1
</pre>
There are several new usages in <a href="../5/#e10">Example 5.10</a>: “te'a” means “raised to the power”, and we also see the use of the lerfu word “ny”, representing the letter “n”. In mekso, letters stand for just what they do in ordinary mathematics: variables. The parser will accept a string of lerfu words (called a “lerfu string”) as the equivalent of a single lerfu word, in agreement with computer-science conventions; “abc” is a single variable, not the equivalent of “a × b × c”. (Of course, a local convention could state that the value of a variable like “abc”, with a multi-lerfu name, was equal to the values of the variables “a”, “b”, and “c” multiplied together.)
<p>The explicit operator “pi'i” is required in the Lojban verbal form whereas multiplication is implicit in the symbolic form. Note that “ve'o” (the right parenthesis) is an elidable terminator: the first use of it in <a href="../5/#e10">Example 5.10</a> is required, but the second use (marked by square brackets) could be elided. Additionally, the first “bi'e” (also marked by square brackets) is not necessary to get the proper grouping, but it is included here for symmetry with the other one.</p>
diff --git a/18/6/index.html b/18/6/index.html
index a2e61ff..241ba9c 100644
--- a/18/6/index.html
+++ b/18/6/index.html
@@ -38,21 +38,21 @@
fy. BY letter “f”
</pre>
<p>The infix form explained so far is reasonable for many purposes, but it is limited and rigid. It works smoothly only where all operators have exactly two operands, and where precedences can either be assumed from context or are limited to just two levels, with some help from parentheses.</p>
<p>But there are many operators which do not have two operands, or which have a variable number of operands. The preferred form of expression in such cases is the use of “forethought operators”, also known as Polish notation. In this style of writing mathematics, the operator comes first and the operands afterwards:</p>
<pre>
<a id="e1" name="e1">6.1)</a> li su'i paboi reboi ci[boi] du li xa
The-number the-sum-of one two three equals the-number six.
sum(1,2,3) = 6
</pre>
Note that the normally elidable number terminator “boi” is required after “pa” and “re” because otherwise the reading would be “pareci” = 123. It is not required after “ci” but is inserted here in brackets for the sake of symmetry. The only time “boi” is required is, as in <a href="../6/#e1">Example 6.1</a>, when there are two consecutive numbers or lerfu strings.
-<p>Forethought mekso can use any number of operands, in <a href="../6/#e1">Example 6.1</a> three. How do we know how many operands there are in ambiguous circumstances? The usual Lojban solution is employed: an elidable terminator, namely “ku'e”. Here is an example:</p>
+<p>Forethought mekso can use any number of operands, in <a href="../6/#e1">Example 6.1</a>, three. How do we know how many operands there are in ambiguous circumstances? The usual Lojban solution is employed: an elidable terminator, namely “ku'e”. Here is an example:</p>
<pre>
<a id="e2" name="e2">6.2)</a> li py. su'i va'a ny. ku'e su'i zy du li xy.
The-number “p” plus negative-of(“n”) plus “z” equals the-number “x”.
p + -n + z = x
</pre>
where we know that “va'a” is a forethought operator because there is no operand preceding it.
<p>“va'a” is the numerical negation operator, of selma'o VUhU. In contrast, “vu'u” is not used for numerical negation, but only for subtraction, as it always has two or more operands. Do not confuse “va'a” and “vu'u”, which are operators, with “ni'u”, which is part of a number.</p>
<p>In <a href="../6/#e2">Example 6.2</a>, the operator “va'a” and the terminator “ku'e” serve in effect as parentheses. (The regular parentheses “vei” and “ve'o” are NOT used for this purpose.) If the “ku'e” were omitted, the “su'i zy” would be swallowed up by the “va'a” forethought operator, which would then appear to have two operands, “ny” and “su'i zy.”, where the latter is also a forethought expression.</p>
<p>Forethought mekso is also useful for matching standard functional notation. How do we represent “z = f(x)”? The answer is:</p>
<pre>
diff --git a/18/7/index.html b/18/7/index.html
index c85ff7f..f8afc00 100644
--- a/18/7/index.html
+++ b/18/7/index.html
@@ -35,21 +35,21 @@
du x1 is identical to x2, x3, x4, ...
dunli x1 is equal/congruent to x2 in/on property/quality/dimension/quantity x3
mleca x1 is less than x2
zmadu x1 is greater than x2
dubjavme'a x1 is less than or equal to x2 [du ja mleca, equal or less]
dubjavmau x1 is greater than or equal to x2 [du ja zmadu, equal or greater]
tamdu'i x1 is similar to x2 [tarmi dunli, shape-equal]
turdu'i x1 is isomorphic to x2 [stura dunli, structure-equal]
cmima x1 is a member of set x2
gripau x1 is a subset of set x2 [girzu pagbu, set-part]
- na'ujbi x1 is approximately equal to [namcu jibni, number-near]
+ na'ujbi x1 is approximately equal to x2 [namcu jibni, number-near]
terci'e x1 is a component with function x2 of system x3
</pre>
Note the difference between “dunli” and “du”; “dunli” has a third place that specifies the kind of equality that is meant. “du” refers to actual identity, and can have any number of places:
<pre>
<a id="e2" name="e2">7.2)</a> py. du xy.boi zy.
“p” is-identical-to “x” “z”
p = x = z
</pre>
Lojban bridi can have only one predicate, so the “du” is not repeated.
<p>Any of these selbri may usefully be prefixed with “na”, the contradictory negation cmavo, to indicate that the relation is false:</p>
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