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<h2 align="center"> </h2>
<h2 align="center">Chapter 12: The Number System</h2>
<div align="center">
<table width="43%" border="0" cellpadding="1" cellspacing="1">
<tr>
<td width="329"><font size="2"><a href="#Sec12o1">12.1 Features of a Centesimal
Number System</a></font></td>
</tr>
<tr>
<td><font size="2"><a href="#Sec12o2">12.2 Semantic Designations for Numerical
Stems </a></font></td>
</tr>
<tr>
<td><font size="2"><a href="#Sec12o3">12.3 Expressing “Zero”</a></font></td>
</tr>
<tr>
<td><font size="2"><a href="#Sec12o4">12.4 Writing Numerals</a></font></td>
</tr>
<tr>
<td><font size="2"><a href="#Sec12o5">12.5 Using Numbers in Speech</a></font></td>
</tr>
</table>
</div>
<p align="justify">The Ithkuil system of numbers and counting is distinct from
Western languages in two fundamental ways: it is centesimal (base one hundred)
as opposed to decimal (base ten), and the numbers themselves are full formatives
(i.e., nouns and verbs), not adjectives. This has already been discussed briefly
in <a href="ithkuil-ch4-case.htm">Section 4.5.7</a> regarding
the <font size="2">PARTITIVE</font> case. This section will examine the numerical
system in greater detail.</p>
<p> </p>
<div align="justify">
<table width="100%" border="0" cellpadding="0" bgcolor="#CCCCCC">
<tr>
<td><p><font size="4"><strong>12.1 FEATURES OF A CENTESIMAL NUMBER SYSTEM<a name="Sec12o1"></a></strong></font></p></td>
</tr>
</table>
</div>
<p align="justify">Being a centesimal system of enumeration, the numbers from
zero to 100 are considered autonomous units represented by single stems and
written using single autonomous symbols. Beginning with the number 101, numbers
are referred to by the number of hundreds plus the number of units, just as
a decimal system, beginning with the number 11, refers to the number of tens
plus the number of units. However, where a decimal system then shifts to a unit
referring to 100 once “10 tens” is reached, a centesimal system
proceeds to the number 10,000 before establishing a new unit reference (i.e.,
“100 hundreds”). Thus the number 3254, which in a decimal system
is 3 thousands — 2 hundreds — 5 tens — 4 ones, in a centesimal
system becomes 32 hundreds—54 ones, and would be only two digits when
written (the single character representing 32, and the single character representing
54). The details of writing Ithkuil numerals are given below in Section 12.5.</p>
<p align="justify">After 100, separate unit numbers and symbols are assigned to
the square of 100 (i.e. ten thousand, that being “100 hundreds”),
then the square of that number, <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1a.gif" width="29" height="16" align="absmiddle">
(100 million, i.e., 10,000 ten-thousands). The final unit is <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1b.gif" width="28" height="15" align="baseline">,
that is, 10 quadrillion or 100 million hundred-millions, the last number for
which Ithkuil assigns a separate root and symbol. After ten quadrillion, numbers
are referred to as multiples of lower sets, similar to saying in English “one
trillion quadrillion” instead of the equivalent “one octillion.”</p>
<p align="justify">While the above may seem unwieldy or even arbitrary, it actually
parallels Western base-ten numerals in terms of its systematization. For example,
in a Western number like 456,321,777,123, each set of three numbers between
the commas tells how many hundreds there are of a certain power of 1000 (i.e.,
there are 123 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1c.gif" width="36" height="15">,
777 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1d.gif" width="35" height="15">,
321 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1e.gif" width="36" height="14">,
and 456 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1f.gif" width="36" height="14">,
or in more common terms 123 ones, 777 thousands, 321 millions, 456 billions).</p>
<p align="justify">The same exact system holds for Ithkuil, except that the sets
of numbers “between the commas” so to speak, is the number of ten-thousands,
not thousands. Thus, if we were to rewrite the Western number 456,321,777,123
in such a system, it would be <strong>4563,2177,7123</strong> (i.e., 7123 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1g.gif" width="49" height="18" align="absmiddle">,
2177 of<font color="#FFFFFF">_<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1h.gif" width="48" height="18" align="absmiddle"></font>,
and 4563 of<font color="#FFFFFF">_<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1i.gif" width="49" height="18" align="absmiddle"></font>,
that being 7123 ones, 2177 ten-thousands, and 4563 hundred-millions). </p>
<p> </p>
<div align="justify">
<table width="100%" border="0" cellpadding="0" bgcolor="#CCCCCC">
<tr>
<td><p><font size="4"><strong>12.2 SEMANTIC DESIGNATIONS FOR NUMERICAL STEMS<a name="Sec12o2"></a></strong></font></p></td>
</tr>
</table>
</div>
<p align="justify">The semantic roots for numbers in Ithkuil from 1 to 99 are
based on roots for 1 through 10, to which the nine degrees of the affix <strong>-V<font size="1">1</font>t’</strong>
are added. Each of the nine degrees of this suffix, when applied to one of the
ten number-roots, corresponds to an additional multiple of ten. This is illustrated
in Table 67 below.<br>
</p>
<p align="justify"><font face="Arial, Helvetica, sans-serif"><strong>Table 67:
The <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2010/10-1-1c.gif" width="34" height="18" align="absmiddle">
Affix with Numerals</strong></font></p>
<p align="justify"><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-2.gif" width="637" height="112"></p>
<p align="justify">The addition of a particular degree of this affix to one of
the ten indicates that the root number is added to that multiple of ten. For
example, the stem <font face="Arial, Helvetica, sans-serif"> <strong>kas</strong></font>
‘two,’ plus the seventh degree affix <strong>-V1t’/7</strong>,
gives <font face="Arial, Helvetica, sans-serif"><strong>kast’ï</strong></font>
‘seventy-two.’ Because there is no root corresponding to ‘zero’
(see <a href="#Sec12o3">Sec. 12.3</a> below), each multiple of ten is constructed using stem <font face="Arial, Helvetica, sans-serif"><strong>mas</strong></font>
‘ten’ plus one of the above suffixes. Thus, the numbers 20, 30 and
40 are respectively <strong><font face="Arial, Helvetica, sans-serif">mast’</font></strong>,
<font face="Arial, Helvetica, sans-serif"> <strong>mast’u</strong></font>
and <font face="Arial, Helvetica, sans-serif"><strong>mast’ai</strong></font>,
but the numbers 22, 32 and 42 are <strong><font face="Arial, Helvetica, sans-serif">kast’u</font></strong>,
<strong> <font face="Arial, Helvetica, sans-serif">kast’ai</font></strong>
and <strong><font face="Arial, Helvetica, sans-serif">kast’ei</font></strong>.
This pattern only operates up to the nineties, as there is a separate autonomous
root for 100, <em><font face="Arial, Helvetica, sans-serif"><strong>r-s</strong></font></em>.</p>
<p align="justify">Since numbers are formatives in Ithkuil, not adjectives as
in most Western languages, holistic stem No. 1, shown by the vocalic infix <font face="Arial, Helvetica, sans-serif"><strong>-a-</strong></font>,
is a formative signifying a set containing a number of members corresponding
to that particular root. Thus, the formative <strong><font face="Arial, Helvetica, sans-serif">kas</font></strong>
above, translatable as ‘two,’ actually means ‘a set of two;
a duo / to be a duo.’ In turn, the two complementary derivatives of each
stem denote its multiple and its fraction respectively. This is illustrated
below for both Form I and II using the roots <font face="Arial, Helvetica, sans-serif"><strong>k-s</strong></font>,
<font size="2">TWO</font>, and <font face="Arial, Helvetica, sans-serif"><strong>n-s</strong></font>,
meaning <font size="2">SEVEN</font>:</p>
<p align="justify">For <strong><font face="Arial, Helvetica, sans-serif">k-s</font></strong>,
<font size="2">TWO</font>:</p>
<p>1. <strong><font face="Arial, Helvetica, sans-serif">kas/kâs</font></strong>
<em>‘a set of two, a duo; to be two in number’</em></p>
<blockquote>
<p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<font face="Arial, Helvetica, sans-serif"><strong>kes/kês</strong></font>:
<em>‘twice the number of something; to double, to multiply by two’</em><br>
<strong><font face="Arial, Helvetica, sans-serif">käs/kaes</font></strong>:
<em>‘a half; to halve, to be or make half, to divide by or in two’</em></p>
</blockquote>
<p>2. <strong><font face="Arial, Helvetica, sans-serif">kus/kûs</font></strong>
<em>‘to be or make dual; having two uses or aspects; bi-; twofold’
</em></p>
<blockquote>
<p><font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<font face="Arial, Helvetica, sans-serif"><strong>kos/kôs</strong></font>:
<em>‘two times (i.e., iterations), twice; to be/do/make twice’</em><br>
<strong><font face="Arial, Helvetica, sans-serif">kös/køs</font></strong>:
<em>‘to be of or make into two parts; bifurcate(d)’</em></p>
</blockquote>
<p>3. <font face="Arial, Helvetica, sans-serif"><strong>kis/kîs</strong></font>
<em>‘the second one in a sequence; to be or make second (in a sequence)’</em></p>
<blockquote>
<p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<font face="Arial, Helvetica, sans-serif"><strong>kës/kÿs</strong></font>:
‘to the second power, squared; to square, raise to the 2nd power<em>’</em><br>
<strong><font face="Arial, Helvetica, sans-serif">küs/kius</font></strong>:
<em>‘to the negative second power, the inverse square; to divide by
the square of’</em></p>
</blockquote>
<p>For <strong><font face="Arial, Helvetica, sans-serif">n-s</font></strong>,
<font size="2">SEVEN</font>:</p>
<p>1. <strong><font face="Arial, Helvetica, sans-serif">nas/nâs</font></strong>
‘a set/group of seven, a septet; to be seven in number’</p>
<blockquote>
<p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<font face="Arial, Helvetica, sans-serif"><strong>nes/nês</strong></font>:
<em>‘7 times the number of something; to multiply by 7; septuple’</em><br>
<strong><font face="Arial, Helvetica, sans-serif">näs/naes</font></strong>:
<em>‘a seventh; to be or make a 7th part of something, to divide by
7 or into 7 parts’</em></p>
</blockquote>
<p>2. <font face="Arial, Helvetica, sans-serif"><strong>nus/nûs</strong></font>
‘to be or make seven-faceted; having 7 uses or aspects; septi-; sevenfold’
</p>
<blockquote>
<p><font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<strong><font face="Arial, Helvetica, sans-serif">nos/nôs</font></strong>:
<em>‘7 times (i.e., iterations); to be/do/make 7 times’</em><br>
<strong><font face="Arial, Helvetica, sans-serif">nös/nøs</font></strong>:
<em>‘to be of or make into 7 parts; separate(d) into 7 parts’</em></p>
</blockquote>
<p>3. <font face="Arial, Helvetica, sans-serif"><strong>nis/nîs</strong></font>
<em>‘the seventh one in a sequence; to be or make 7th (in a sequence)’
</em> </p>
<blockquote>
<p><font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<font face="Arial, Helvetica, sans-serif"><strong>nës/nÿs</strong></font>:
<em>‘to the 7th power; to raise to the 7th power’ </em><br>
<strong><font face="Arial, Helvetica, sans-serif">nüs/nius</font></strong>:
<em>‘to the negative 7th power; to divide by the 7th power of’
</em> </p>
</blockquote>
<p align="justify">In addition to the above-described roots, there is the root
<font face="Arial, Helvetica, sans-serif"><strong>l-s</strong></font>, <font size="2">ONE/UNITY</font>.
As this root has no multiples, its semantic designations follow a unique pattern.
<font size="2">NOTE</font>: The <font size="2">INFORMAL</font> versus <font size="2">FORMAL</font>
distinction in this root (i.e., Form I versus Form II of each stem) distinguishes
between a focus on non-duplication/singularity for the <font size="2">INFORMAL</font>,
and indivisibility/unity for the <font size="2">FORMAL</font>:</p>
<p> 1. <strong><font face="Arial, Helvetica, sans-serif">las/lâs</font></strong>
<em>‘a single entity; to be one in number’ </em></p>
<blockquote>
<p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<strong><font face="Arial, Helvetica, sans-serif">les/lês</font></strong>:
<em>‘to be indivisible, whole, a single unit; unitary; to unify’</em><br>
<font face="Arial, Helvetica, sans-serif"><strong>läs/laes</strong></font>:
<em>‘to be (an) individual, a distinct entity in itself; to individualize’</em></p>
</blockquote>
<p>2. <strong><font face="Arial, Helvetica, sans-serif">lus/lûs</font></strong>
‘a lone entity, something alone; an entity in solitude, something/someone
isolated; be alone; to isolate; be in solitude’</p>
<blockquote>
<p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<strong><font face="Arial, Helvetica, sans-serif">los/lôs</font></strong>:
<em>‘something/someone lonely; be or make lonely’</em><br>
<font face="Arial, Helvetica, sans-serif"><strong>lös/løs</strong></font>:
<em>‘something/someone independent, self-sufficient, singular (i.e.,
without need of, connection to, or dependency on others); be or make independent,
self-sufficient, singular’</em></p>
</blockquote>
<p>3. <font face="Arial, Helvetica, sans-serif"><strong>lis/lîs</strong></font>
‘something/someone unique, the only one; to be or make unique’</p>
<blockquote>
<p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br>
<strong><font face="Arial, Helvetica, sans-serif">l</font><font face="Arial, Helvetica, sans-serif">ës/lÿs</font></strong>:
<em>‘a sole entity, the only one available or able (in terms of sufficiency
or applicability to the context)’</em><br>
<font face="Arial, Helvetica, sans-serif"><strong>lüs/lius</strong></font>:
<em>‘something/someone one-of-a-kind, unparalleled, without equal or
peer (in terms of uniqueness of characteristics)’</em></p>
</blockquote>
<p><br>
The Ithkuil numerical roots as described in the section above are as follows:</p>
<table width="75%" border="1" cellpadding="1">
<tr>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">l-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">k-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">š-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">p-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif"><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%201/Symbols/t-cedilla.gif" width="7" height="16" align="absbottom">-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">t-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">n-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">x-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">
f-s</font></strong></div></td>
<td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">m-s</font></strong></div></td>
</tr>
<tr>
<td><div align="center"><em>one</em></div></td>
<td><div align="center"><em>two</em></div></td>
<td><div align="center"><em>three</em></div></td>
<td><div align="center"><em>four</em></div></td>
<td><div align="center"><em>five</em></div></td>
<td><div align="center"><em>six</em></div></td>
<td><div align="center"><em>seven</em></div></td>
<td><div align="center"><em>eight</em></div></td>
<td><div align="center"><em>nine</em></div></td>
<td><div align="center"><em>ten</em></div></td>
</tr>
</table>
<br>
<table width="75%" border="1" cellpadding="1">
<tr>
<td width="19%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">r-s</font></strong></div></td>
<td width="22%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">q-s</font></strong></div></td>
<td width="27%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">ç-s</font></strong></div></td>
<td width="32%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">c-s</font></strong></div></td>
</tr>
<tr>
<td><div align="center"><em>one hundred</em></div></td>
<td><div align="center"><em>ten thousand</em></div></td>
<td><div align="center"><em>one hundred million</em></div></td>
<td><div align="center"><em>ten quadrillion</em></div></td>
</tr>
</table>
<p> </p>
<table width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC">
<tr>
<td><p><font size="4"><strong>12.3 EXPRESSING “ZERO” <a name="Sec12o3"></a></strong></font></p></td>
</tr>
</table>
<p align="justify"> Ithkuil has no word for “zero” nor is it conceptualized
as a numerical category. Instead any appropriate formative may take the affixes
-V1ss/1 or -V2ss/1 <em>‘no amount of’</em> or -V3b/1 <em>‘no…at
all’</em> in terms of degree or extent to create negative expressions
that convey the idea of an absence of a numerical entity or quantity. In many
cases, simply the negative of whatever formative is under discussion may be
used. </p>
<p align="justify">As for handling the concept of zero as a null placeholder when
writing Ithkuil numbers, this is addressed in Section 12.4 below.</p>
<p> </p>
<table width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC">
<tr>
<td><p><font size="4"><strong>12.4 WRITING NUMERALS<a name="Sec12o4"></a></strong></font></p></td>
</tr>
</table>
<p align="justify">Writing Ithkuil numerals is somewhat similar to writing numbers
in Western languages (i.e., “Arabic” numerals), in that the interpretation
of a number as a different power of 100 (analogous to interpreting single Arabic
numerals as either ones, tens, hundreds, thousands, etc.) is based on its sequence
within the entire number. However, there are two aspects of writing Ithkuil
numbers that are quite different from Arabic numbers.:</p>
<ol>
<li>
<div align="justify">Ithkuil does not employ a symbol for zero. Instead, Ithkuil
employs separate autonomous symbols for each power of 100 (100, 10,000,
100 million, etc.) each of which operates as the appropriate placeholder
instead of zero. To illustrate what this means by analogy, pretend that
“@” is an autonomous symbol for 27 (since Ithkuil numbers from
1 to 99 each have a separate symbol), “&” is a symbol for
100, “#” is a symbol for 10,000 and there is no symbol 0 (zero).
The numbers 2700, 2705, 327, 22700 and 4,270,027 would then be written @&,
@5, 3@, 2@&, and 4@#@ respectively. (NOTE: In actual practice, numbers
which contain the “hundred” symbol, here represented as “&,”
normally place a dot above or below the adjacent numeral and dispense with
the &, indicating that the number so marked is to be multiplied by 100.
Thus, 2@& would actually be written as <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4a.gif" width="23" height="30" align="top">,
while ‘one million’ can be written as <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4b.gif" width="9" height="26" align="top">
instead of writing &#.<br>
</div>
</li>
<li>
<div align="justify">Since Ithkuil is a base-100 system, numbers do not become
two digits in length until the hundreds, do not become three digits in length
until the ten thousands, do not become four digits in length until the millions,
etc.</div>
</li>
</ol>
<p align="justify"> </p>
<p align="justify">One must also remember that in terms of left-to-right or up-and-down
orientation, numbers follow the <em>boustrophedon</em> mode the same as the
Ithkuil script (see <a href="ithkuil-ch11-script.htm">Sec. 11.3.2</a>).
Similarly to Western languages, small non-compound numbers can be written using
either their numerical symbols or written out in script (as in English “12”
versus “twelve”).</p>
<p align="justify">The following table gives the Ithkuil numerical symbols along
with their morphological stems:<br>
<br>
<font face="Arial, Helvetica, sans-serif"><strong>Table 68: ITHKUIL NUMERICAL
STEMS AND WRITTEN SYMBOLS</strong></font><br>
<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4c.gif" width="639" height="621"> <br>
<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4d.gif" width="639" height="681"><br>
<br>
<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4e.gif" width="320" height="135"></p>
<p> </p>
<table width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC">
<tr>
<td><p><font size="4"><strong>12.5 USING NUMBERS IN SPEECH<a name="Sec12o5"></a></strong></font></p></td>
</tr>
</table>
<p align="justify">Spoken numbers are formed from the above stems using both the
<font size="2">PARTITIVE</font> and <font size="2">COMITATIVE</font> cases,
as well as using the coordinative affix <strong>-V<font size="1">1</font>w/1</strong>
(= <strong><font face="Arial, Helvetica, sans-serif">-iw</font></strong> or
<font face="Arial, Helvetica, sans-serif"><strong>-wai</strong></font>). The
number of largest base units is shown by placing the base-unit term in the <font size="2">PARTITIVE</font>.
If this is then followed by another collection of smaller base units, that number
of smaller base units is connected using the <font size="2">COMITATIVE</font>
case while the smaller base-unit term is again in the <font size="2">PARTITIVE</font>.
Single units (from 1 to 99) are connected by the coordinative affix when they
are part of the number of hundreds or higher base-units. </p>
<p align="justify">It should be noted that when pronouncing numbers greater than
199, it is normal in Ithkuil to omit the word <font face="Arial, Helvetica, sans-serif"><strong><em>ra’wirs</em></strong></font>
(= the <font size="2">PARTITIVE</font> of <strong><font face="Arial, Helvetica, sans-serif">ras</font></strong>
‘one hundred’) referring to the number of hundreds. This is equivalent
to the custom in colloquial English of saying ‘three twelve’ for
‘three hundred (and) twelve.’ The difference is that in Ithkuil,
this omission of the word for ‘hundred’ is the preferred option,
the word <em>ra’wirs</em> being used only in larger numbers for clarity’s
sake.</p>
<p align="justify">These principles are illustrated by the following examples:</p>
<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5a.gif" width="165" height="74"><br>
literally: “42 (of hundreds) 29”<br>
<em><strong>4229</strong></em> <br>
</p>
<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5b.gif" width="285" height="75"><br>
literally: “26 of ten-thousands with 97 (of hundreds) 66” = 26,9766<font color="#FFFFFF"></font><br>
<em><strong>269,766<br>
</strong></em><strong><font size="1" face="Arial, Helvetica, sans-serif"><a href="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Sound_Files/Ch-12-1.mp3">Listen!</a>
</font></strong><em><strong><font size="1" face="Arial, Helvetica, sans-serif"><a href="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Sound_Files/Ch-12-1.mp3"><img src="Audio_icon.gif" width="19" height="16" border="0" align="absbottom"></a></font></strong></em></p>
<p> </p>
<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5c.gif" width="159" height="73"><br>
literally: “21 of hundred of ten-thousands”<br>
<strong><em>21,000,000</em></strong> <br>
[NOTE: <em>ra’wirs</em> is required in this example]</p>
<p><br>
<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5d.gif" width="651" height="72"><br>
literally: <br>
“72 of hundreds and 79 of hundred-millions with 3 of hundreds and 53 of
ten-thousands with 34 of hundreds 60” <br>
<strong>727,903,533,460</strong></p>
<p align="justify"><br>
We have already seen that when numbers are used to indicate how many of a certain
noun there are, the noun must appear in the <font size="2">PARTITIVE</font>
case, since the number itself is functioning as the “head” of the
numerical expression (e.g., English “12 boxes” being constructed
in Ithkuil as a “12-set of a box” or perhaps more appropriately
a “box-dozen”). Another syntactical consequences of numbers being
full formatives is when a number functions as a label or overt identifier, as
in the English sentence <em>You’ll find him in Room 216.</em> Such usage
of numbers is not primarily sequential (which would involve the equivalent of
“ordinal” numbers such as ‘fourth,’ ‘twenty-sixth’,
etc. equivalent to stem No. 3 of each number root) but rather organizational
(e.g., as in the three-dimensional array of room numbers in a hotel). Ithkuil
handles such organizational labeling using either the <font size="2">CONTRASTIVE</font>
case (see <a href="ithkuil-ch4-case.htm">Sec. 4.5.6</a>) or
the <font size="2">ESSIVE</font> case (see <a href="ithkuil-ch4-case.htm">Sec.
4.6.1</a>) depending respectively on whether the enumeration of the noun in
question is to distinguish it from other enumerated nouns versus merely identifying
the noun by a numerical name. Examples:</p>
<p><br>
<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5e.gif" width="124" height="63"> <br>
<em>‘the room marked “12”’ </em><font size="2"><strong>OR</strong></font><em>
‘Room 12’ </em><font size="2"><strong>OR</strong></font><em> ‘Room
No. 12’</em> [i.e., as distinguished from the other numbered rooms]</p>
<p><br>
<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5f.gif" width="126" height="61"> <br>
<em>‘the room marked “12”’ </em><font size="2"><strong>OR</strong></font><em>
‘Room 12’ </em><font size="2"><strong>OR</strong></font><em> ‘Room
No. 12’</em> [identifying reference only]</p>
<p align="justify"><br>
Lastly, when numbers comprising multiple number-stems are declined for case,
configuration, extension, etc., rather than writing out the entire number “long-hand,”
the number symbol is used, preceded by the carrier stem <em><strong>kir</strong></em>
(see <a href="ithkuil-ch9-syntax.htm">Sec. 9.4</a>) which carries the appropriate
declensions. This use of the carrier stem applies even to single-stemmed numbers
when writing, in order to allow use of the number symbol instead of writing
it out. In such cases involving single-stemmed numbers, the carrier stem is
not pronounced (rather, the numerical stem bears the pronounced declensions);
it is there only as a written indicator of the declensions to be applied to
the number stem. Thus, the above two examples could also be written as: </p>
<p></p>
<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5g.gif" width="135" height="47"> <font color="#FFFFFF">_________________<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5h.gif" width="129" height="51"></font></p>
<p align="justify"> </p>
<p>
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<td width="37%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch5a-verbs.htm">5a
Verb Morphology </a></font></div></td>
<td width="27%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch9-syntax.htm">9
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<td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-intro.htm">Introduction</a></font></div></td>
<td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch5b-verbs-contd.htm">5b
Verb Morphology (continued)</a></font></div></td>
<td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch10-lexicosemantics.htm">10
Lexico-Semantics</a></font></div></td>
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<td valign="top"><div align="left"><font size="2"></font><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch1-phonology.htm">1
Phonology</a></font></div></td>
<td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch6-moreverbs.htm">6
More Verb Morphology</a></font></div></td>
<td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch11-script.htm">11
The Script </a></font></font></div></td>
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<td height="26" valign="top"> </td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch2-morphophonology.htm">2
Morpho-Phonology</a></font><font size="2"> </font></td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch7a-affixes.htm">7a
Using Affixes </a></font></font></font></td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch12-numbers.htm">12
The Number System</a></font></font></font></td>
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<td height="26" valign="top"> </td>
<td valign="top"><font size="2"> </font><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch3-morphology.htm">3
Basic Morphology</a></font></td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch7b-affixes-contd.htm">7b
Using Affixes (continued) </a></font></font></td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-lexicon.htm">The
Lexicon</a></font></font></td>
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<td height="26" valign="top"> </td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch4-case.htm">4
Case Morphology </a></font> </td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch8-adjuncts.htm">8
Adjuncts</a></font></td>
<td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="Ilaksh_Intro.html" target="_blank">Revised Ithkuil: <font face="Times New Roman, Times, serif">I</font>laksh</a></font></td>
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