generated from smyalygames/quartz
70 lines
4.9 KiB
XML
70 lines
4.9 KiB
XML
<?xml version="1.0" encoding="UTF-8" ?>
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<rss version="2.0">
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<title>ACIT4330 Lecture Notes</title>
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<link>https://https://acit4330.pages.anthonyberg.io/</link>
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<description>Last 10 notes on ACIT4330 Lecture Notes</description>
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<generator>Quartz -- quartz.jzhao.xyz</generator>
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<item>
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<title>Cauchy-Schwarz Inequality</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Schwarz-Inequality</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Schwarz-Inequality</guid>
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<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>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>ACIT4330 Table of Contents</title>
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<link>https://https://acit4330.pages.anthonyberg.io/</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/</guid>
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<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>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Least Upper Bound Property</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Least-Upper-Bound-Property</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Least-Upper-Bound-Property</guid>
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<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>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>And</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/And</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/And</guid>
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<description>P \land Q Truth Table PQ=FFFFTFTFFTTT.</description>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Implies</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Implies</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Implies</guid>
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<description>P \implies Q Truth Table PQ=FFTFTTTFFTTT.</description>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Not</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Not</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Not</guid>
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<description>¬P The symbol (¬) is called negation Truth Table P=FTTF.</description>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Subnet</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Subnet</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Subnet</guid>
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<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') \geq i \; \forall j' \geq j ...</description>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Cauchy Sequence</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Sequence</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Cauchy-Sequence</guid>
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<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>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Nets</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Nets</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Nets</guid>
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<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>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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</item><item>
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<title>Or</title>
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<link>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Or</link>
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<guid>https://https://acit4330.pages.anthonyberg.io/Definitions/Statements/Or</guid>
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<description>P \lor Q Truth Table PQ=FFFFTTTFTTTT.</description>
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<pubDate>Sat, 01 Mar 2025 15:59:38 GMT</pubDate>
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