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      <text>3.0.5 (Purpose of Proof)</text>
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      <text><![CDATA[<h1>The purpose of proof</h1>

<p>We have seen that mathematical proof is key in developing new mathematical techniques and argument. However there are several other reasons that proof is key to maths.</p>
<p>Proof is used: </p>

<ul style="list-style: none;">
<li>To convince the reader of the truth or falsity of a given statement. This becomes particularly important when the result of the statement seems counterintuitive. This is a far more common occurrence in maths than one would initially expect.</li>
<li>To understand how and why the different assumptions, definitions and hypotheses interact and combine to make the result.</li>
<li>To communicate new ideas or Theorems. Mathematicians talk the language of proof, it is the cornerstone of mathematical discourse and debate.</li>
<li>To discover new ideas and new mathematics. This is the process of mathematical research.</li>
</ul>

<p>A proof is an example of <i>deductive reasoning</i>, we begin at some starting point, under some assumptions often taking the form of definitions or statements, we then apply a sequence of mathematical or logical steps to arrive at a conclusion which is another mathematical statement.</p>]]></text>
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