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basics2.html
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<!DOCTYPE html>
<head>
<meta charset="utf-8">
<meta name="description" content="A book about education, technology, mathematics, computers and programming for humans."/>
<meta name="keywords" content="education, technology, mathematics, programming, humans"/>
<meta name="author" content="Shiv Shankar Dayal" />
<meta name="copyright" content="Shiv Shankar Dayal" />
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<title>Humans, education and technology</title>
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<span class="mdc-toolbar__title"><a href="/" class="menu-anchor">Home</a></span>
<span class="mdc-toolbar__title"><a href="toc.html" class="menu-anchor">Table of Contents</a></span>
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<section>
<h2>One or Truth</h2>
<p>
Our next symbol is one or \(1\). Following the logical deduction we
can say that if zero represents the concept of false or absence then
one must represent truth or presence. But it also represents something
more. It represents count of an object.
</p>
<h3>Counting</h3>
<p>
As you are most probably aware of counting symbols which are \(0, 1, 2,
3, 4, 5, 6, 7, 8, 9\) form the decimal number system we use. Since
\(1\) is used as a truth value we make \(2\) from \(1\). So let us
say you and me are present in the same room. You are one human and I am
also one human. But when a third person wants to know about how many
persons are present in here then the answer would be \(2\) persons.
Thus, we can say the some operation has to be performed on the count
of individual humans to arrive at that number \(2\). This operation
is known as addition and immediately the symbols \(+\) flashes in
front of our open eyes or in our mind. Our mind is so trained at this
association that it is instantaneous.
</p>
<p>
I would like to describe addition but before that let me present
number axis.
<svg width="400" height="100" viewBox="-40 -10 450 90"
xmlns="http://www.w3.org/2000/svg">
<line x1="0" y1="0" x2="400" y2="0"
stroke-width="1" stroke="green"/>
<line x1="200" y1="-10" x2="200" y2="10"
stroke-width="1" stroke="green"/>
<text x="-10" y="35" font-size="25">
-∞
</text>
<line x1="1" y1="-10" x2="1" y2="10"
stroke-width="1" stroke="green"/>
<text x="195" y="35" font-size="20">
0
</text>
<line x1="400" y1="-10" x2="400" y2="10"
stroke-width="1" stroke="green"/>
<text x="385" y="35" font-size="25">
∞
</text>
<line x1="230" y1="-10" x2="230" y2="10"
stroke-width="1" stroke="green"/>
<text x="225" y="35" font-size="20">
1
</text>
<line x1="260" y1="-10" x2="260" y2="10"
stroke-width="1" stroke="green"/>
<text x="255" y="35" font-size="20">
2
</text>
<line x1="170" y1="-10" x2="170" y2="10"
stroke-width="1" stroke="green"/>
<text x="165" y="35" font-size="20">
-1
</text>
<text x="150" y="75" font-size="20">
Number axis
</text>
</svg>
</p>
<p>
Now as you see two new symbols. \(-\) is called minus as you
are probably aware and represents negative values. But hang on
for a while. The other symbol is very important. It is called
infinity and we use \(\infty\) to denote it.
</p>
<p>
So what is infinity. It is a concept. You see that as you count
from \(0\) to \(9\) you understand that count will never end.
Infinity is a conceptual and mathematical end of counting process.
</p>
<p>
So you measure distance between \(0\) and \(1\) and if you move
the same distance towards \(\infty\) then you will arrive at
\(2\) and similarly if you repeat this step then you will arrive
at \(9\). What after that?
</p>
<p>
We need more symbols but we just cannot have infinite symbols to
represent each and every number. So we reuse symbols available to
us. To represent the number after \(9\) we use two of the smallest
symbols \(0\) and \(1\). It could be written like \(10\) or \(01\)
depending on whether you write left-to-right or right-to-left.
Since this system is supposedly developed in India it makes sense
to write it as \(10\). \(0\) is used to boost the value of \(1\).
So you continue till \(99\). Then again repeat the process and
count till \(100\) to \(999\) and then \(1000\) to \(9999\) so you
see that it is a never ending process.
</p>
<p>
A sharp person will observe that \(1\) is smallest single-digit
number which has value as \(0\) is just absence so we cannot use it
to represent a value. \(9\) is largest single digit number. Similarly,
\(10\) and \(99\) represents smallest and largest two-digit numbers.
</p>
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