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content/index.md

@@ -1,3 +1,7 @@
+---
+title: ACIT4330 Table of Contents
+---
+
 # Chapter 1
 ## 1.1 Sets and Numbers
 - [[Lecture 1 - 1.1 Sets and Numbers]] (complimentary written notes: [[ACIT4330-2025-01-06-Lecture 1.rnote]])

public/index.xml

@@ -10,61 +10,61 @@
     <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Schwarz-Inequality</link>
     <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Schwarz-Inequality</guid>
     <description>Definition | (u|v) | \leq \| \, u \, \|_{2} \times \| \, v \, \|_{2} \| \, u + v \, \|_{2} \leq \| \, u \, \|_{2} + \| \, v \, \|_{2} Proof of Cauchy-Schwartz Insert a \equiv - \frac{\overline{(u ...</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
+  </item><item>
+    <title>ACIT4330 Table of Contents</title>
+    <link>https://https://acit4330.pages.anthonyberg.io/</link>
+    <guid>https://https://acit4330.pages.anthonyberg.io/</guid>
+    <description>Chapter 1 1.1 Sets and Numbers Lecture 1 - 1.1 Sets and Numbers (complimentary written notes: ACIT4330-2025-01-06-Lecture 1.rnote) Lecture 2 (complimentary written notes: ACIT4330-2025-01-09-Lecture ...</description>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
   </item><item>
     <title>Least Upper Bound Property</title>
     <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Least-Upper-Bound-Property</link>
     <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Least-Upper-Bound-Property</guid>
     <description>X \subset \mathbb{R} \exists c \in \mathbb{R} \; \text{such that} x \lt c, \forall x \in X sup(\langle 0, 1 \rangle) = 1 \notin \langle 0, 1 \rangle sup(\langle 0, 1 ] \,) sup(\mathbb{R}) ...</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
-  </item><item>
-    <title>Not</title>
-    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Not</link>
-    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Not</guid>
-    <description>¬P The symbol (¬) is called negation Truth Table P=FTTF.</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
-  </item><item>
-    <title>Subnet</title>
-    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Subnet</link>
-    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Subnet</guid>
-    <description>Definition A subnet of a net f: I \to X is a net g: J \to X and a map h : J \to I such that g = f \circ h and such that \forall i \in I \exists j \in J with h(j&#039;) \geq i \; \forall j&#039; \geq j ...</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
-  </item><item>
-    <title>index</title>
-    <link>https://https://acit4330.pages.anthonyberg.io/</link>
-    <guid>https://https://acit4330.pages.anthonyberg.io/</guid>
-    <description>Chapter 1 1.1 Sets and Numbers Lecture 1 - 1.1 Sets and Numbers (complimentary written notes: ACIT4330-2025-01-06-Lecture 1.rnote) Lecture 2 (complimentary written notes: ACIT4330-2025-01-09-Lecture ...</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
-  </item><item>
-    <title>Cauchy Sequence</title>
-    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Sequence</link>
-    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Sequence</guid>
-    <description>Definition A Cauchy sequence is a sequence where the elements become arbitrarily close to each other as the sequence progresses. Examples Cauchy Sequence \Sigma_{n=1}^\infty \frac{1}{n^2} = 1, \, \frac{1}{4}, \, \frac{1}{9}, \, \dots \lim_{ n \to \infty } \frac{1}{n^2} = 0 Which this sequence converges to 0, towards infinity Non-Cauchy Sequence \Sigma_{n=1}^{\infty}(-1)^n = -1, \, 1, \, -1, \, 1, \, \dots These never converge to a limit, hence it is not Cauchy.</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
-  </item><item>
-    <title>Nets</title>
-    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Nets</link>
-    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Nets</guid>
-    <description>\{ x_{i} \}_{i \in I} \; \text{NET} \; \underbrace{I}_{\text{VFOs}} \to X x \in \overline{X} \iff \exists \; \text{NET} \; \underbrace{x_{i}}_{\in X} \to x I = neighbourhoods of ...</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
   </item><item>
     <title>And</title>
     <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/And</link>
     <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/And</guid>
     <description>P \land Q Truth Table PQ=FFFFTFTFFTTT.</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
   </item><item>
     <title>Implies</title>
     <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Implies</link>
     <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Implies</guid>
     <description>P \implies Q Truth Table PQ=FFTFTTTFFTTT.</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
+  </item><item>
+    <title>Not</title>
+    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Not</link>
+    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Not</guid>
+    <description>¬P The symbol (¬) is called negation Truth Table P=FTTF.</description>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
+  </item><item>
+    <title>Subnet</title>
+    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Subnet</link>
+    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Subnet</guid>
+    <description>Definition A subnet of a net f: I \to X is a net g: J \to X and a map h : J \to I such that g = f \circ h and such that \forall i \in I \exists j \in J with h(j&#039;) \geq i \; \forall j&#039; \geq j ...</description>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
+  </item><item>
+    <title>Cauchy Sequence</title>
+    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Sequence</link>
+    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Sequence</guid>
+    <description>Definition A Cauchy sequence is a sequence where the elements become arbitrarily close to each other as the sequence progresses. Examples Cauchy Sequence \Sigma_{n=1}^\infty \frac{1}{n^2} = 1, \, \frac{1}{4}, \, \frac{1}{9}, \, \dots \lim_{ n \to \infty } \frac{1}{n^2} = 0 Which this sequence converges to 0, towards infinity Non-Cauchy Sequence \Sigma_{n=1}^{\infty}(-1)^n = -1, \, 1, \, -1, \, 1, \, \dots These never converge to a limit, hence it is not Cauchy.</description>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
+  </item><item>
+    <title>Nets</title>
+    <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Nets</link>
+    <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Nets</guid>
+    <description>\{ x_{i} \}_{i \in I} \; \text{NET} \; \underbrace{I}_{\text{VFOs}} \to X x \in \overline{X} \iff \exists \; \text{NET} \; \underbrace{x_{i}}_{\in X} \to x I = neighbourhoods of ...</description>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
   </item><item>
     <title>Or</title>
     <link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Or</link>
     <guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Or</guid>
     <description>P \lor Q Truth Table PQ=FFFFTTTFTTTT.</description>
-    <pubDate>Sat, 01 Mar 2025 15:39:56 GMT</pubDate>
+    <pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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   </url><url>
     <loc>https://https://acit4330.pages.anthonyberg.io/Definitions/Vector-Spaces/Complex-Vector-Space</loc>
-    <lastmod>2025-03-01T15:39:56.363Z</lastmod>
+    <lastmod>2025-03-01T15:59:38.419Z</lastmod>
   </url><url>
     <loc>https://https://acit4330.pages.anthonyberg.io/Definitions/Vector-Spaces/Linear-Basis</loc>
-    <lastmod>2025-03-01T15:39:56.363Z</lastmod>
+    <lastmod>2025-03-01T15:59:38.419Z</lastmod>
   </url><url>
     <loc>https://https://acit4330.pages.anthonyberg.io/Definitions/Vector-Spaces/Normed-Vector-Space</loc>
-    <lastmod>2025-03-01T15:39:56.364Z</lastmod>
+    <lastmod>2025-03-01T15:59:38.419Z</lastmod>
   </url><url>
     <loc>https://https://acit4330.pages.anthonyberg.io/Definitions/Vector-Spaces/Properties-of-a-Vector-Space</loc>
-    <lastmod>2025-03-01T15:39:56.363Z</lastmod>
+    <lastmod>2025-03-01T15:59:38.419Z</lastmod>
   </url><url>
     <loc>https://https://acit4330.pages.anthonyberg.io/Lectures/Lecture-1---1.1-Sets-and-Numbers</loc>
     <lastmod>2025-01-06T00:00:00.000Z</lastmod>
@@ -204,5 +204,5 @@
     <lastmod>2025-02-03T00:00:00.000Z</lastmod>
   </url><url>
     <loc>https://https://acit4330.pages.anthonyberg.io/</loc>
-    <lastmod>2025-03-01T15:39:56.368Z</lastmod>
+    <lastmod>2025-03-01T15:59:38.426Z</lastmod>
   </url></urlset>