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diff --git a/.doctrees/assets/index.doctree b/.doctrees/assets/index.doctree
diff --git a/.doctrees/assets/notes/algebra.doctree b/.doctrees/assets/notes/algebra.doctree
diff --git a/.doctrees/assets/notes/algebra_09.10.2023.doctree b/.doctrees/assets/notes/algebra_09.10.2023.doctree
diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
diff --git a/assets/index.html b/assets/index.html
@@ -132,9 +132,59 @@ <h4>składanie funkcji<a class="headerlink" href="#skladanie-funkcji" title="Lin
 h(x) &amp;= g(f(x))\\
 h &amp;= g \cdot f\\
 \end{split}\]</div>
+<p><em>Notatki z pliku <code class="docutils literal notranslate"><span class="pre">notes/algebra.md</span></code></em></p>
 </section>
 </section>
 </section>
+</section>
+<section class="tex2jax_ignore mathjax_ignore" id="algebra">
+<h1>ALGEBRA<a class="headerlink" href="#algebra" title="Link to this heading">¶</a></h1>
+<p><em>Notatki z pliku <code class="docutils literal notranslate"><span class="pre">notes/algebra_09.10.2023.md</span></code></em></p>
+<section id="zestaw-1-zadanie-5">
+<h2>Zestaw 1 zadanie 5<a class="headerlink" href="#zestaw-1-zadanie-5" title="Link to this heading">¶</a></h2>
+<p>Korzystając z zas. indukcji udowodnij że:
+dla dowolnego <span class="math notranslate nohighlight">\(n \in \mathbb{N}, n &gt;= 4\)</span> liczba diagonalnych
+w n-koncie wypukłym jest niewiększa niż <span class="math notranslate nohighlight">\(\frac{1}{2} n(n-3)\)</span></p>
+<ul class="simple">
+<li><p>utworzenie wzoru na liczbę diagonalnych</p>
+<ul>
+<li><p>dla 4-kątu jest to  <code class="docutils literal notranslate"><span class="pre">1</span></code></p></li>
+<li><p>dla 5-kątu - <code class="docutils literal notranslate"><span class="pre">2</span></code></p></li>
+<li><p>dla 6-kątu - <code class="docutils literal notranslate"><span class="pre">3</span></code></p></li>
+</ul>
+</li>
+</ul>
+<p>z tego wniosek, że liczba diagonalnych <span class="math notranslate nohighlight">\(d = n-3\)</span></p>
+<ul class="simple">
+<li><p>sprawdzenie warunku dla n = 4</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+n-3 &lt;= \frac{1}{2} n (n - 3)\\
+dla n = 4\\
+1 &lt;= 2 * 1
+\end{split}\]</div>
+<ul class="simple">
+<li><p>krok indukcyjny</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+załóżmy, że: \\
+\frac{1}{2}n (n-3) &gt;= n-3 \\
+n (n-3) &gt;= 2n-6 \\
+n^2 - 3n &gt;= 2n-6 \\
+n^2 - 5n + 6 &gt;= 0 \\
+wtedy dla n+1:\\
+\frac{1}{2}(n+1)(n-2) &gt;= n-2 \\
+n^2-n-2 &gt;= 2n-4 \\
+n^2-3n+2 &gt;= 0 \\
+(n^2-5n+2) + (2n - 4) &gt;= 0\\
+\begin{matrix}
+(n^2-5n+2) + &amp; (2n - 4) &amp; &gt;= 0\\
+z ind mat.   &amp; \forall n &gt;= 4 2n - 4 &gt;=0 &amp;
+\end{matrix}
+\end{split}\]</div>
+</section>
 </section>
 
 
@@ -158,6 +208,10 @@ <h3><a href="../index.html">Spis treści:</a></h3>
 </li>
 </ul>
 </li>
+<li><a class="reference internal" href="#algebra">ALGEBRA</a><ul>
+<li><a class="reference internal" href="#zestaw-1-zadanie-5">Zestaw 1 zadanie 5</a></li>
+</ul>
+</li>
 </ul>
 
   </div>

diff --git a/assets/notes/algebra.html b/assets/notes/algebra.html
@@ -0,0 +1,128 @@
+
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+    <title>ALGEBRA &#8212; Matematyka  - dokumentacja</title>
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+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="Indeks ogólny"
+             accesskey="I">indeks</a></li>
+    <li><a href="../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">ALGEBRA</a></li> 
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+  <section class="tex2jax_ignore mathjax_ignore" id="algebra">
+<h1>ALGEBRA<a class="headerlink" href="#algebra" title="Link to this heading">¶</a></h1>
+</section>
+
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+             >indeks</a></li>
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diff --git a/assets/notes/algebra_09.10.2023.html b/assets/notes/algebra_09.10.2023.html
@@ -0,0 +1,172 @@
+
+
+<!DOCTYPE html>
+
+<html lang="pl" data-content_root="../../">
+  <head>
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+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
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+    <title>Zestaw 1 zadanie 5 &#8212; Matematyka  - dokumentacja</title>
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+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="Indeks ogólny"
+             accesskey="I">indeks</a></li>
+    <li><a href="../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">Zestaw 1 zadanie 5</a></li> 
+      </ul>
+    </div>
+    </div>
+
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+
+  <section id="zestaw-1-zadanie-5">
+<h1>Zestaw 1 zadanie 5<a class="headerlink" href="#zestaw-1-zadanie-5" title="Link to this heading">¶</a></h1>
+<p>Korzystając z zas. indukcji udowodnij że:
+dla dowolnego <span class="math notranslate nohighlight">\(n \in \mathbb{N}, n &gt;= 4\)</span> liczba diagonalnych
+w n-koncie wypukłym jest niewiększa niż <span class="math notranslate nohighlight">\(\frac{1}{2} n(n-3)\)</span></p>
+<ul class="simple">
+<li><p>utworzenie wzoru na liczbę diagonalnych</p>
+<ul>
+<li><p>dla 4-kątu jest to  <code class="docutils literal notranslate"><span class="pre">1</span></code></p></li>
+<li><p>dla 5-kątu - <code class="docutils literal notranslate"><span class="pre">2</span></code></p></li>
+<li><p>dla 6-kątu - <code class="docutils literal notranslate"><span class="pre">3</span></code></p></li>
+</ul>
+</li>
+</ul>
+<p>z tego wniosek, że liczba diagonalnych <span class="math notranslate nohighlight">\(d = n-3\)</span></p>
+<ul class="simple">
+<li><p>sprawdzenie warunku dla n = 4</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+n-3 &lt;= \frac{1}{2} n (n - 3)\\
+dla n = 4\\
+1 &lt;= 2 * 1
+\end{split}\]</div>
+<ul class="simple">
+<li><p>krok indukcyjny</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+załóżmy, że: \\
+\frac{1}{2}n (n-3) &gt;= n-3 \\
+n (n-3) &gt;= 2n-6 \\
+n^2 - 3n &gt;= 2n-6 \\
+n^2 - 5n + 6 &gt;= 0 \\
+wtedy dla n+1:\\
+\frac{1}{2}(n+1)(n-2) &gt;= n-2 \\
+n^2-n-2 &gt;= 2n-4 \\
+n^2-3n+2 &gt;= 0 \\
+(n^2-5n+2) + (2n - 4) &gt;= 0\\
+\begin{matrix}
+(n^2-5n+2) + &amp; (2n - 4) &amp; &gt;= 0\\
+z ind mat.   &amp; \forall n &gt;= 4 2n - 4 &gt;=0 &amp;
+\end{matrix}
+\end{split}\]</div>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../genindex.html" title="Indeks ogólny"
+             >indeks</a></li>
+    <li><a href="../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">Zestaw 1 zadanie 5</a></li> 
+      </ul>
+    </div>
+    </div>
+
+    <div class="footer" role="contentinfo">
+    &#169; Copyright 2023, Maciej Sz.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.6.
+    </div>
+    <!-- cloud_sptheme 1.4 -->
+  </body>
+</html>
diff --git a/index.html b/index.html
@@ -80,6 +80,10 @@ <h1>Wstęp<a class="headerlink" href="#wstep" title="Link to this heading">¶</a
 <li class="toctree-l2"><a class="reference internal" href="assets/index.html#funkcja">Funkcja</a></li>
 </ul>
 </li>
+<li class="toctree-l1"><a class="reference internal" href="assets/index.html#algebra">ALGEBRA</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="assets/index.html#zestaw-1-zadanie-5">Zestaw 1 zadanie 5</a></li>
+</ul>
+</li>
 </ul>
 </div>
 <div class="admonition important">

diff --git a/objects.inv b/objects.inv