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<h1 class="title">The Book</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgheadline4">1. (</a>
<ul>
<li><a href="#orgheadline1">1.1. Topics To Be Explored</a></li>
<li><a href="#orgheadline2">1.2. Autobiographical Aside</a></li>
<li><a href="#orgheadline3">1.3. TOP is the TLA</a></li>
</ul>
</li>
<li><a href="#orgheadline29">2. ONE</a>
<ul>
<li><a href="#orgheadline10">2.1. ABC</a>
<ul>
<li><a href="#orgheadline5">2.1.1. GIK</a></li>
<li><a href="#orgheadline6">2.1.2. MOQ</a></li>
<li><a href="#orgheadline7">2.1.3. SUW</a></li>
<li><a href="#orgheadline8">2.1.4. YAC</a></li>
<li><a href="#orgheadline9">2.1.5. EGI</a></li>
</ul>
</li>
<li><a href="#orgheadline22">2.2. DEF</a>
<ul>
<li><a href="#orgheadline11">2.2.1. KMO</a></li>
<li><a href="#orgheadline12">2.2.2. QSU</a></li>
<li><a href="#orgheadline13">2.2.3. WYA</a></li>
<li><a href="#orgheadline14">2.2.4. CEG</a></li>
<li><a href="#orgheadline15">2.2.5. IKM</a></li>
<li><a href="#orgheadline16">2.2.6. OQS</a></li>
<li><a href="#orgheadline17">2.2.7. UWY</a></li>
<li><a href="#orgheadline18">2.2.8. BDF</a></li>
<li><a href="#orgheadline19">2.2.9. HJL</a></li>
<li><a href="#orgheadline20">2.2.10. NPR</a></li>
<li><a href="#orgheadline21">2.2.11. TVX</a></li>
</ul>
</li>
<li><a href="#orgheadline28">2.3. GHI</a>
<ul>
<li><a href="#orgheadline23">2.3.1. ZBD</a></li>
<li><a href="#orgheadline24">2.3.2. FHJ</a></li>
<li><a href="#orgheadline25">2.3.3. LNP</a></li>
<li><a href="#orgheadline26">2.3.4. RTV</a></li>
<li><a href="#orgheadline27">2.3.5. XZB</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgheadline53">3. TWO</a>
<ul>
<li><a href="#orgheadline32">3.1. JKL</a>
<ul>
<li><a href="#orgheadline30">3.1.1. DFH</a></li>
<li><a href="#orgheadline31">3.1.2. JLN</a></li>
</ul>
</li>
<li><a href="#orgheadline47">3.2. MNO</a>
<ul>
<li><a href="#orgheadline33">3.2.1. PRT</a></li>
<li><a href="#orgheadline34">3.2.2. VXZ</a></li>
<li><a href="#orgheadline35">3.2.3. ADG</a></li>
<li><a href="#orgheadline36">3.2.4. JMP</a></li>
<li><a href="#orgheadline37">3.2.5. SVY</a></li>
<li><a href="#orgheadline38">3.2.6. BEH</a></li>
<li><a href="#orgheadline39">3.2.7. KNQ</a></li>
<li><a href="#orgheadline40">3.2.8. TWZ</a></li>
<li><a href="#orgheadline41">3.2.9. CFI</a></li>
<li><a href="#orgheadline42">3.2.10. LOR</a></li>
<li><a href="#orgheadline43">3.2.11. UXA</a></li>
<li><a href="#orgheadline44">3.2.12. DGJ</a></li>
<li><a href="#orgheadline45">3.2.13. MPS</a></li>
<li><a href="#orgheadline46">3.2.14. VYB</a></li>
</ul>
</li>
<li><a href="#orgheadline52">3.3. PQR</a>
<ul>
<li><a href="#orgheadline48">3.3.1. EHK</a></li>
<li><a href="#orgheadline49">3.3.2. NQT</a></li>
<li><a href="#orgheadline50">3.3.3. WZC</a></li>
<li><a href="#orgheadline51">3.3.4. FIL</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgheadline66">4. THR</a>
<ul>
<li><a href="#orgheadline59">4.1. STU</a>
<ul>
<li><a href="#orgheadline54">4.1.1. ORU</a></li>
<li><a href="#orgheadline55">4.1.2. XAD</a></li>
<li><a href="#orgheadline56">4.1.3. GJM</a></li>
<li><a href="#orgheadline57">4.1.4. PSV</a></li>
<li><a href="#orgheadline58">4.1.5. YBE</a></li>
</ul>
</li>
<li><a href="#orgheadline62">4.2. VWX</a>
<ul>
<li><a href="#orgheadline60">4.2.1. HKN</a></li>
<li><a href="#orgheadline61">4.2.2. QTW</a></li>
</ul>
</li>
<li><a href="#orgheadline65">4.3. YZ@</a>
<ul>
<li><a href="#orgheadline63">4.3.1. ZCF</a></li>
<li><a href="#orgheadline64">4.3.2. ILO</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#orgheadline67">5. )</a></li>
<li><a href="#orgheadline68">6. GNU Free Documentation License</a></li>
</ul>
</div>
</div>
<p>
<i>Metaphors Be With You: A Tireless Work On Play On Words</i>
</p>
<div class="figure">
<p><a href="https://rickneff.github.io/img/tineless.png"><img src="https://rickneff.github.io/img/tinelessTN.png" alt="tinelessTN.png" /></a>
</p>
</div>
<p>
Copyright © 2015 Richard Madsen Neff
</p>
<p>
Permission is granted to copy, distribute and/or modify this
document under the terms of the GNU Free Documentation License,
Version 1.3 or any later version published by the Free Software
Foundation; with the Invariant Sections being "(", with the
Front-Cover Texts being "Metaphors Be With You: A Tireless Work On
Play On Words", and no Back-Cover Texts.
</p>
<p>
A copy of the license is included in the section entitled ‘‘GNU
Free Documentation License’’.
</p>
<p>
-~-~-~-~-~-
</p>
<dl class="org-dl">
<dt>To my Dad</dt><dd><p>
for inspiring me to get 'er done.
</p>
<p>
-~-~-~-~-~-
</p></dd>
</dl>
<div id="outline-container-orgheadline4" class="outline-2">
<h2 id="orgheadline4"><span class="section-number-2">1</span> (</h2>
<div class="outline-text-2" id="text-1">
<p>
Groucho Marx once quipped, "Outside of a dog, a book is a man's best
friend. Inside of a dog, it's too dark to read." <a href="#orgtarget1">This book is not
about that kind of word play</a>. (These are not the droids you're
looking for. Move on.) But it <i>will</i> have something to say about
<i>Outside</i> versus <i>Inside</i> in a logical context later on.
</p>
<p>
Kith and kin to word play is the idea of transformation, new from
old. Old is known, new unknown. The unknown is daunting unless and
until it becomes known. And the becoming process is called learning,
a transformation from an old state of (less) knowledge to a new state
of (more) knowledge.
</p>
</div>
<div id="outline-container-orgheadline1" class="outline-3">
<h3 id="orgheadline1"><span class="section-number-3">1.1</span> Topics To Be Explored</h3>
<div class="outline-text-3" id="text-1-1">
<p>
The field of knowledge called discrete mathematics is <b>HUGE</b> —
and no wonder; it is like a catch-all net. Anything not
contemplated by mathematics of the continuous variety (calculus and
company) is considered discrete (but not discreet). So narrowing
the scope is a challenge of near epic proportions — met by
allowing the following topic pairs to serve as guideposts as we
venture out into this vast field.
</p>
<ol class="org-ol">
<li>Sets and Logic</li>
<li>Functions and Relations</li>
<li>Combinatorics and Probability</li>
<li>Number Theory and Practice</li>
<li>Trees and Graphs</li>
<li>Languages and Grammars</li>
</ol>
<p>
Functions (which build on sets (which build on logic)) embody
transformations. These are natural, foundational topics in a study
of discrete mathematics. And to provide a transformative learning
experience, functional programming (the oft-neglected (by most
students) odd duck of the programming world) will be a particular
focus of this work.
</p>
<p>
There are two main reasons to gain experience with the functional
paradigm. One, functional programming <a href="#orgtarget2">rounds out the dyad</a>
of procedural and object-oriented programming, presumably already
in the typical programmer's toolbox. Two, learning functional
programming is a natural way to learn discrete mathematics,
especially since functions are a key aspect, and illuminate many
other aspects of discrete mathematics.
</p>
<p>
For reasons revealed à la <a href="#orgtarget3">Isaiah 28:10</a>, the language of choice for
learning functional programming will be the <b>lisp</b> programming
language, specifically the Emacs lisp (elisp) dialect. Why lisp,
certainly, but especially why elisp? To forestall unbearable
suspense, let's dispense with the knee-jerk objection that elisp is
not a <b>pure</b> functional programming language. With discipline it
can be used as such, and the effort will be instructive.
</p>
<p>
<a href="#orgtarget4">A quick review and preview</a>:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="all" frame="border">
<colgroup>
<col class="org-left" />
</colgroup>
<colgroup>
<col class="org-left" />
</colgroup>
<colgroup>
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Procedural</th>
<th scope="col" class="org-left">Object-Oriented</th>
<th scope="col" class="org-left">Functional</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Variable values vary.</td>
<td class="org-left">Same as Procedural.</td>
<td class="org-left">Variable values never change once assigned.</td>
</tr>
<tr>
<td class="org-left">Collections are mutable.</td>
<td class="org-left">Same as Procedural.</td>
<td class="org-left">Collections are immutable.</td>
</tr>
<tr>
<td class="org-left">Code is stateful (function calls can have side effects).</td>
<td class="org-left">Same as Procedural.</td>
<td class="org-left">Code is stateless (function calls can be replaced by their return values without changing program behavior).</td>
</tr>
<tr>
<td class="org-left">Functions are partial (not defined on all inputs, so exceptions can be thrown).</td>
<td class="org-left">Same as Procedural.</td>
<td class="org-left">Functions are total (defined on all inputs, so exceptions are not thrown, and need not be handled.)</td>
</tr>
</tbody>
</table>
<p>
The above table doesn't capture all the distinctions in this
three-way comparison, but one thing is obvious. When looked at
through the functional lens, procedural and object-oriented are the
same. What then distinguishes them? Mainly what types can
be the values of variables. Object-oriented adds user-defined types
to the standard primitives and composites of procedural.
</p>
<p>
P-L and O-O also differ on how they treat nouns and verbs. It gets
pretty topsy-turvy when normal everyday distinctions between nouns
(things) and verbs (actions) are blurred. When not only do nouns get
verbed, but verbs get nouned, we have a double play on words!
</p>
<p>
Speaking of double, combinatorics, the study of combining, or
counting, and number theory, the study of integers (useful for
counting — especially the positive ones) are an integral ☺
part of discrete math. How many ways are there of combining things
in various combinations? Variations, arrangements, shufflings —
these are things that must be accounted for in the kind of careful
counting that is foundational for discrete probability theory. But
they also come into play in modern practices of number theory like
cryptology, the study of secret messages.
</p>
<p>
Double encore: two more discrete structures, with a cornucopia of
applications, are trees and their generalization, graphs. Trees and
graphs are two of the most versatile and useful data structures ever
invented, and will be explored in that light.
</p>
<p>
Teaser begin, a <b>binary</b> tree — perhaps the type easiest to
understand — can represent <a href="#orgtarget5">any conceptual (as opposed to
botanical) tree</a> whatsoever. How to do so takes us into deep
representational waters, but we'll proceed carefully. And because
graphs can represent relations, listed above in conjunction with
functions, they truly are rock solid stars of math and computer
science. The relationship between functions and relations is like
that of trees and graphs, and when understood leads to starry-eyed
wonder, end teaser.
</p>
<p>
Last double: finishing off and rounding out this relatively small
set of topics is the dynamic duo, languages and grammars. Language
is being used, rather prosaically, as a vehicle for communication,
even as I write these words, and you read them. There is fascinating
scientific evidence for the facility of language being innate,
inborn, a human instinct. Steven Pinker, who literally wrote the
book on this, calls language a "discrete combinatorial system",
which is why it makes total sense that it be in this book and
beyond.
</p>
<p>
And what is grammar? Pinker in his book is quick to point out what
it is not. Nags such as "Never end a sentence with a preposition,"
"Don't dangle participles," and (my personal favorite) "To ever
split an infinitive — anathema!" Such as these are what you may
have learned in "grammar school" as teachers tried their best to
drill into you how to use good English. No doubt my English teachers
would cringe at reading the last phrase of the last sentence of the
last paragraph, where "it" is used in two different ways, and "this
book" can ambiguously refer to more than one referent — think
about it.
</p>
<p>
No, in the context of discrete mathematics, grammar has nothing to
do with proper English usage. Instead, a grammar (note the
indefinite article) is a <b>generator</b> of the discrete combinations
of the language system. These generated combinations are called
<b>phrase structures</b> (as opposed to word structures), hence, in this
sense grammars are more precisely known as <b>phrase structure
grammars</b>. But we're getting ahead of ourselves — <a href="#orgtarget6">PSG ISA TLA TBE l8r</a>.
</p>
</div>
</div>
<div id="outline-container-orgheadline2" class="outline-3">
<h3 id="orgheadline2"><span class="section-number-3">1.2</span> Autobiographical Aside</h3>
<div class="outline-text-3" id="text-1-2">
<p>
I am writing this book for many reasons, which mostly relate to the
following language-ish math-ish relationships and transformations:
Words have Letters, Numbers have Digits, Letters map to Digits,
hence Words map to Numbers.
</p>
<p>
I love words. I love numbers. Does that mean English was my first
choice of discipline, Math second? No! English is my native tongue,
but Math to me feels PRE native, or the language I came into this
world furnished with. Not that I lay claim to being a mathematical
prodigy like Fredrich Gauss, John Von Neumann, or any extraordinary
human like that. Not even close!
</p>
<p>
A first recollection of my inchoate interest in math is from third
grade. There I was, standing at the blackboard, trying to figure
out multiplication. The process was mysterious to me, even with my
teacher right there patiently explaining it. But her patience paid
off, and when I "got it" the thrill was electrifying! Armed with a
memorized times table, I could wield the power of this newly
acquired understanding. Much later in life came the realization
that I could immensely enjoy helping others acquire understanding
and thus wield power!
</p>
<p>
Back to words. As I said, I love them. I love the way words work. I
love the way they look. I love the way they sound. Part of this
stems from my love of music, especially vocal music. Singers pay
attention to nuances of pronunciation, <a href="#orgtarget7">5</a> being but one
example. Take another example. The rule for pronouncing the e in
the. Is it ee or uh? It depends not on the look of the next word
but its sound. The honorable wants ee not uh because the aitch is
silent. The Eternal, but the One — ee, uh. Because one is
actually won.
</p>
<p>
The attentive reader may have noticed that, among other
infelicities, the preceding paragraph plays fast and loose with
<b>use</b> versus <b>mention</b>. There is a distinction to be made between
the use of a word, and the mention of a word.
</p>
<p>
For example, the word <b>Idaho</b>:
</p>
<p>
Idaho has mountains. (A use of the word.)
</p>
<p>
'Idaho' has five letters. (A mention of the word.)
</p>
<p>
This distinction will come to the fore when expressions in a
programming language like lisp must be precisely formed and
evaluated. The quote marks are all-important. Small marks, big
effect.
</p>
<p>
Analogously, what importance does a simple preposition have? How
about the crucial difference between being saved <b>in</b> your sins
versus being saved <b>from</b> your sins! Small words, enormous effect.
</p>
<p>
I have a well-nigh fanatical fondness for the English alphabet with
its 26 letters. 26 is 2 times 13. 2 and 13 are both prime, which is
cool enough, but they're also my birth month and day. And it's
unambiguous which is which. 2/13 or 13/2 — take your
pick. Because there's no thirteenth month, either way works. Not
every birth date is so lucky! <a href="#orgtarget8">Not every language's alphabet is so easy</a>, either.
</p>
<p>
Despite the coolness of twice a baker's dozen, it is deficient by
one of being an even cooler multiple of three, and that's a state
of affairs we'll not long tolerate. But which non-alphabetic (and
non-numeric) symbol is best pressed into service to bring the
number to three cubed?
</p>
<p>
Twenty-seven is three times nine. Nine give or take three is the
number of main topics. Three chapters (not counting opening and
closing bookends), with each chapter having at least three
sections, each section having at least three subsections —
perhaps bottoming out at this level — this seems to me to be a
pretty good organization.
</p>
<p>
Slice it. Dice it. No matter how you whatever ice it — notice
it's not ice (but is it water — whatever hve u dehydrated?!) —
'<a href="#orgtarget9">alphabet</a>' is one letter shy of being a <i>concatenation</i>
(smooshing together) of the first two letters of some other
(which?) alphabet. So correct its shyness (and yours). Say
alphabeta. Go ahead, say it! Now say ALP HAB ETA (each is
pronounceable) — but don't expect anyone to understand what you
just said!
</p>
</div>
</div>
<div id="outline-container-orgheadline3" class="outline-3">
<h3 id="orgheadline3"><span class="section-number-3">1.3</span> TOP is the TLA</h3>
<div class="outline-text-3" id="text-1-3">
<p>
The Organizing Principle I have chosen for this book is the
Three-Letter Acronym.
</p>
<p>
Why? Well, it fully fascinates me that "TLA ISA" is a perfectly
grammatical sentence if interpreted just so. It expresses concisely
the truth: 'TLA' "self-describes" (which is another intriguing
saying).
</p>
<p>
But TLA can also stand for Three-Letter Abbreviation, of which
there are many, <code>(JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC)</code>
being but one example.
</p>
<p>
Replacing the 'A' in TLA with a 'W' gives TLW, an acronym for
Three-Letter Word — <code>(TOP TOE TON TOT TOY)</code> for a butcher's
half-dozen of which.
</p>
<p>
Note that we could generate this list by simply prefixing <code>TO</code> to
each letter in <a href="#orgtarget10"><code>PENTY</code>, a carefully chosen way to code-say Christmas</a>.
</p>
<p>
Note too that neither this list of five TLWs nor the first list of
twelve TLAs has commas, those typical list item separators. The
comma-free rendering is deliberate and significant, as will be
seen.
</p>
<p>
Back to playing with words. If you can eat your words, shouldn't
you be able to smell and taste them too?! Or play with words like
you play with your food? (These are rhetorical questions —
don't try to answer them!)
</p>
<p>
Scrambled <code>EGGS</code> — <code>(GSGE GESG SGEG ...)</code>
</p>
<p>
Can all 12 (not 24! (which is NOT to say 24 factorial (which equals
620448401733239439360000, <a href="#orgtarget11">IYI</a>))) arrangements be put into
one tetragramamalgam? What's a tetragramamalgam? (These are
NOT rhetorical questions — DO try to answer them!)
</p>
<p>
So there you have it. An assorted set of words and "words" to guide
discovery. Many to unpack meaning from. If the metaphor is a good
one, that meaning gets packed into words, (or encodings thereof
(another layer of packing material)), then unpacking can result in
rich interconnected structures that strengthen learning, that make
it stick in the brain. And that that permanently (it is hoped)
stuck learning will serve you well <a href="#orgtarget12">is my high hope</a>.
</p>
</div>
</div>
</div>
<div id="outline-container-orgheadline29" class="outline-2">
<h2 id="orgheadline29"><span class="section-number-2">2</span> ONE</h2>
<div class="outline-text-2" id="text-2">
<p>
<a href="#orgtarget13">He awoke with a start</a>. What time was it? … Did his alarm
not go off? … No, it was 3:45, he just woke up too early. He lay
there, mind racing, trying to figure out what had woken him up. His
wife was breathing deeply, she was sound asleep, so it wasn't her
stirring. No … it was that dream. That awesome, awefull dream
where he was outside staring into the clear night sky, basking in
"the icy air of night" when suddenly he felt a very real vertigo, as
if he were falling <i>up</i> into that endless star-sprinkled void.
</p>
<p>
Falling up. A contradiction in terms. Yes, but one to be embraced,
not shunned, because it gives one an <a href="#orgtarget14">EDGE</a>. No, this is the title of
a book. Yes, that treasured book <a href="#orgtarget15">he had acquired years ago</a>, and
still enjoyed. Clever poems and cute drawings. It was because the
author was so playful with words and the thoughts they triggered
that he liked it, and his other book, what was it? Where The
Sidewalk Ends. Yes, well, enough of that. He would have to get up
soon. Today he would meet his two new tutees. TWOtees for short. A
male and a female had seen his ad and responded. Was he expecting
more than two to? Yes … but two would be fine. Two would be enough
to keep him busy.
</p>
<p>
-~-~-~-~-~-
</p>
<p>
"What I'd like to do today is just make introductions and see where
we're at," he said. "My name is Tiberius Ishmael Luxor, but you can
call me Til. T-I-L, my initials, my preference." While escorting his
two visitors into his study, his mind wandered, as it always did
when he introduced himself. Tiberius, why had his parents, fervent
fans of Captain Kirk and all things Star Trek, named him that? And
Ishmael? Was Moby Dick also a source of inspiration? Or the Bible?
He had never asked them, to his regret. Luxor, of course, was not a
name they had chosen. He rather liked his family name. The first
three letters, anyway. Latin for light. He often played with Luxor
by asking himself, Light or what? Darkness? Heavy? Going with the
other meaning of light seemed frivolous.
</p>
<p>
"Uh, my name's Atticus. Atticus Bernhold Ushnol," his male visitor
said, noticing that Til looked distracted. "What do you prefer we
call you?" asked Til, jerking himself back to full attention. "Well,
I like Abu, if that's okay with you!"
</p>
<p>
Til smiled. A man after his own heart. "How acronymenamored of
you!" he said.
</p>
<p>
"Is that even a word?" asked his female guest, addressing
Til. Feeling just a little annoyed, she turned to Abu and said "You
really want us to call you the name of the monkey in Aladdin?" Abu
smiled, a crooked grin. "Well, I wouldn't know about that — I
never saw Aladdin."
</p>
<p>
"How could you not have seen Aladdin? What planet are you from?"
she said, completely incredulous.
</p>
<p>
"Hold on a minute," said Til. "Let's discuss the finer points of
names and origins after you introduce yourself."
</p>
<p>
"Ila. My middle name is my maiden name, Bowen. My last name is my
married name, Toopik, which I suppose I'm stuck with." Ila always
felt irritated that marriage traditionally involved changing the
woman's name, not the man's. "And yes, it's Eee-la, not Eye-la. And
I especially prefer you don't call me Ibt, if you get my drift!"
</p>
<p>
Til laughed. Abu was still grinning but said nothing, so Til went
on. "We need variety, so Ila is fine. Not everyone needs to be
acronymized!"
</p>
<p>
-~-~-~-~-~-
</p>
<p>
Later that day as Til reflected on their first meeting, he saw
himself really enjoying the teacher-learner interactions to
come. His ad had had the intended effect. Abu and Ila were
motivated learners, albeit for different reasons. He was somewhat
surprised that not more interest had been generated. But he knew it
was unlikely up front. So two it would be. Two is a good
number. Three is even better (odd better?) if he counted himself as
a learner. Which he always did. Learning and teaching were
intricately intertwined in his mind. Teaching was like breathing,
and both teaching and learning were exhilarating to Til.
</p>
<p>
His wife interrupted his reverie. "Til, dear, what did you learn
today from your first meeting with — what did you call them —
Abu and Ila?"
</p>
<p>
"Interesting things," said Til. "Abu is the general manager at a
landscaping company (I think he said nursery as well). Ila works
for some web design company (I forget the name) doing programming.
She wants to learn discrete math because she's been told it will
make her a better programmer!"
</p>
<p>
"However, Abu's not a programmer, and not really all that techy, I
gathered, but says he <i>loves</i> learning, practical or not. I
predict this may put him at odds at times with Ila, who said she
<i>only</i> wants practical learning. I told her Euclid would mock
that attitude, and she was surprised. But she agreed to look into
that. She didn't know who Euclid was, if you can imagine!" Til
winked his eye, and his wife rolled hers.
</p>
<p>
"Anyway, Abu's pretty laid back, so her barbs won't bother him —
much I hope," he said.
</p>
<p>
"Are they married, any kids?" she said.
</p>
<p>
"Abu is single, but would like to be married." Til rubbed his
chin. "Ila is married, but she didn't mention her husband's name, or
really anything about him, except that he's not a nerd like
her. Before they even warmed up to my affinity for acronyms, Ila
confessed to being a <a href="#orgtarget16">DINK</a>, and Abu immediately responded, 'I guess
that makes me a <a href="#orgtarget17">SINKNEM</a>!' So he's pretty quick on the uptake."
</p>
<p>
"That's good!" she said. "So Ila's husband is not nerdy like her,
but …?"
</p>
<p>
"But she also didn't say what he does," he said. "She taught herself
programming, how cool is that?!"
</p>
<p>
"Very cool, Mr. Luxor," she said affectionately, gently rubbing
his shoulders.
</p>
<p>
"Mrs. Luxor, I'll give you 20 minutes to stop that!" he said.
</p>
<p>
"What are their interests other than discrete math?" she said,
ignoring his pathetic ploy.
</p>
<p>
"Well, let's see, Abu rattled off his other interests as flowers,
stars and poetry!" he said. "And Ila likes sports and the
outdoors. Hopefully that includes stars!"
</p>
<p>
"That would be great if you all have stars in common," she said.
</p>
<p>
Til nodded, but his eyes unfocused as his thoughts started to
wander. His wife withdrew, wordlessly worrying that Til was thinking
about sharing his dream about falling up into the stars with Abu and
Ila. That never seemed to go well. But Til was remembering the
exchange he had with Abu, who lingered a few minutes after Ila left.
</p>
<p>
He had said, "Abu, since you like flowers, you must be okay with
the <a href="#orgtarget18">STEM</a>less reputation they have!" Without waiting for
him to answer he went on, "Since I gave Ila an invitation to learn
something about Euclid, I invite you to look up what Richard
Feynman said about flowers and science, specifically whether
knowing the science made him <a href="#orgtarget19">appreciate the flowers more or less?</a>"
</p>
<p>
Well, enough musing for now. His two tutees were eager and
grateful, and not just because they thought the fee he had set was
reasonable. Little did they know the price of knowledge he would
exact of them.
</p>
<p>
-~-~-~-~-~-
</p>
<div class="figure">
<p><img src="https://rickneff.github.io/img/desert.jpg" alt="desert image" title="What is this doing here?!" />
</p>
</div>
</div>
<div id="outline-container-orgheadline10" class="outline-3">
<h3 id="orgheadline10"><span class="section-number-3">2.1</span> <a href="#orgtarget38">ABC</a></h3>
<div class="outline-text-3" id="text-2-1">
<p>
When you read you begin with A, B, C; when you sing you begin with
Do, Re, Mi; when you count you begin with 1, 2, 3 — or is it 0,
1, 2?! Mathematicians do both, and have logical reasons for
each. Computer scientists mainly do zero-based counting, as coaxed
to do by both hardware and software. 0-1-2; ready-set-goo!
</p>
<p>
So let's begin with the set of positive integers, also known as the
counting numbers — except, wait. How do you count the number of
elements in the set with no elements, <a href="#orgtarget20">AKA</a> the empty set?
You need zero, which for centuries was not even considered a
number. Lucky for us, these days zero is a full-fledged member of
the set of <b>natural</b> numbers, another name for the counting
numbers. But some still see zero as UNnatural and thus exclude it
from the set. Right away, ambiguity rears its hoary head, and
definitions must needs be clarified before crafting arguments that
depend on whether zero is in or out.
</p>
<p>
<a href="#orgtarget21">VTO</a>: a <b>set</b> is just a <b>collection</b> of <b>objects</b>, where
objects are individual, discrete, separate things that can be named
or identified somehow. A collection that serves <a href="#orgtarget22">the mathematical idea of a set</a>
is an <b>unordered</b> one — the elements can be listed in any order
and it doesn't change the set.
</p>
<p>
Speaking of lists, LISP originally stood for LISt Processor (or
Processing), so let's list some simple sets in lisp style, and show
a side-by-side comparison with math style:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="all" frame="border">
<colgroup>
<col class="org-left" />
</colgroup>
<colgroup>
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Lisp Style</th>
<th scope="col" class="org-left">Math Style</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">() or nil</td>
<td class="org-left">{} or ∅</td>
</tr>
<tr>
<td class="org-left">(A B C)</td>
<td class="org-left">{A, B, C}</td>
</tr>