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Infinity.php
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Infinity.php
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<?php
include 'core/init.php';
include 'includes/overall/header.php';
?>
<html>
<body>
<br>
<div class="row">
<div class="col-md-2"></div>
<div class="col-md-8">
<div class="panel panel-default">
<div class="panel-body">
<div class="page-header " style = "margin-top:5px; ">
<h3> Infinity </h3>
</div>
<div class="thumbnail">
<img src="pics/Hilbert_curve.svg" alt="html5" height="210" width="600">
</div>
<div class="page-body" style = "margin-top:5px; ">
<p style='font-size:120%'>
Infinity is a concept that is alien to any living thing because it would never be able to experience such a number.
However, our minds are able to imagine the concept of something having no limits. Is this concept as rediculous as
a children's fairy tale? Or is there truth in believing such a concept? These are very deep philosophical questions
that may not have a direct answer. But guess what? Mathematicians have addressed each hypothetical, and have deduced
many things from believing or not believing in such a thing being posible. Today, most mathematicians take the existence
of infinity as a fact because it gives results to problems effectively. More importantly in mathematics, it has been proven
that the belief or non-belief of the concept of infinity of the consistency of mathematical interpretation.
</p>
<br><br>
<p style='font-size:120%'>
Now, let us talk about some examples of what mathematicians have been known to do that relates to infinity in fields called
Combinatorics and Set Theory. How to count an infinite set. A good example of this is Hilbert's paradox of the Grand Hotel.
This is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully
occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and that
this process may be repeated infinitely often. This brings better understanding to how infinite sets can be counted using
the notion of the existence of a one-to-one correspondence illustrated below.
</p>
<br><br>
<center><img src="pics/2000px-Bijection.svg.png" alt="html5" height="210" width="210"></center>
<br><br>
<p style='font-size:120%'>
The notion of one-to-one correspondence is basically when you uniquely pair up elements from both sets without leaving any
not paired. For example, the below illustration shows that you can pair up every point on the circle that is not the point A
with every point on the line because line segment that connects point A with a point on the line has a unique point of
intersection with the circle that is not the point A.
</p>
</div>
<br>
<center><img src="pics/file.gif" alt="html5" height="210" width="600"></center>
</div>
</div>
</div>
<div class="col-md-2"></div>
</div>
</body>
</html>
<?php include 'includes/overall/footer.php';?>