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Meest verkochte samenvattingen voor Understanding Analysis
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Algebraic Limit Theorem and Order Limit Theorem
- College aantekeningen • 3 pagina's • 2023 Populair
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Explain and provide proof for the algebraic limit theorem and the order limit theorem. Use proof by contradiction for the assumption and conclusion of the two sequences.
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Compact Sets
- College aantekeningen • 4 pagina's • 2023 Populair
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Introduce and provide proof for compact sets, that is a set that is both bounded and closed, hence the Heine-Borel theorem. Then introduce the perfect set, the connected/disconnected sets, and lastly the canter set, write proofs for all three.
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Sequences
- College aantekeningen • 2 pagina's • 2023 Populair
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Introduce sequences and its epsilon proof. Define the convergence of an to a and how to prove it with a backwards proof by first identifying the candidate for the limit and prove that that is the candidate, then prove convergence. Then introduce some theorems about sequences, namely the algebraic limit theorem and the order limit theorem.
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Consequences of Axiom of Completeness
- College aantekeningen • 1 pagina's • 2023 Populair
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Explain the proof for the nested interval property, and also the proofs for the Archimedean Property, which is split into two parts.
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Limit of Sequence
- College aantekeningen • 2 pagina's • 2023 Populair
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Give an epsilon proof for the limit of a sequence, where in more detail the partial sum of a series and its convergence is explained and tested with the p-series test. Then, introduce the Cauchy sequence and the monotone convergence theorem.
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Sequences
- College aantekeningen • 3 pagina's • 2023 Populair
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Introduce sequences and its epsilon proof. Then explain sequences with the algebraic limit theorem and the order limit theorem. Write proof for the theorem that a sequence converges if and only if that sequence is a Cauchy sequence.
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Consequences from Axiom of Completeness Continued.
- College aantekeningen • 3 pagina's • 2023 Populair
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Explain and prove more consequences from the axiom of completeness. First, the density of rational numbers in real numbers using Archimedean principle 1 and axiom of completeness. Then prove the existence of the square root of 2 with contradiction. Lastly, the sequences argument with the algebraic limit theorem and order limit theorem.
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Sequences and Topology of R
- College aantekeningen • 4 pagina's • 2023 Populair
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Finish the lecture on sequences and the convergence of Cauchy. Then introduce the topology of R and in it the epsilon neighborhood of a in R. Define open sets, limit points, isolated points, and closed subsets.
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Axiom of Completeness and Consequences
- College aantekeningen • 3 pagina's • 2023 Populair
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Introduce Axiom of Completeness, the bed rock of advanced calculus, where every nonempty bounded above subset of R has a lower upper bound (supremum), and every nonempty bounded below subset of R has a greatest lower bound (infimum). Introduce the consequences of the Axiom of Completeness, with the Nested Interval Property and the Archimedean Property.
Nieuwste samenvattingen van Understanding Analysis
-
Compact Sets
- College aantekeningen • 4 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Introduce and provide proof for compact sets, that is a set that is both bounded and closed, hence the Heine-Borel theorem. Then introduce the perfect set, the connected/disconnected sets, and lastly the canter set, write proofs for all three.
-
Sequences and Topology of R
- College aantekeningen • 4 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Finish the lecture on sequences and the convergence of Cauchy. Then introduce the topology of R and in it the epsilon neighborhood of a in R. Define open sets, limit points, isolated points, and closed subsets.
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Sequences
- College aantekeningen • 3 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Introduce sequences and its epsilon proof. Then explain sequences with the algebraic limit theorem and the order limit theorem. Write proof for the theorem that a sequence converges if and only if that sequence is a Cauchy sequence.
Schrijf jij zelf ook samenvattingen? Bied deze dan te koop aan en verdien per keer dat je document wordt gekocht.
-
Consequences from Axiom of Completeness Continued.
- College aantekeningen • 3 pagina's • 2023 Nieuw
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- €9,24
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Explain and prove more consequences from the axiom of completeness. First, the density of rational numbers in real numbers using Archimedean principle 1 and axiom of completeness. Then prove the existence of the square root of 2 with contradiction. Lastly, the sequences argument with the algebraic limit theorem and order limit theorem.
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Axiom of Completeness and Consequences
- College aantekeningen • 3 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
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- €9,24
- + meer info
Introduce Axiom of Completeness, the bed rock of advanced calculus, where every nonempty bounded above subset of R has a lower upper bound (supremum), and every nonempty bounded below subset of R has a greatest lower bound (infimum). Introduce the consequences of the Axiom of Completeness, with the Nested Interval Property and the Archimedean Property.
-
Algebraic Limit Theorem and Order Limit Theorem
- College aantekeningen • 3 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Explain and provide proof for the algebraic limit theorem and the order limit theorem. Use proof by contradiction for the assumption and conclusion of the two sequences.
-
Sequences
- College aantekeningen • 2 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Introduce sequences and its epsilon proof. Define the convergence of an to a and how to prove it with a backwards proof by first identifying the candidate for the limit and prove that that is the candidate, then prove convergence. Then introduce some theorems about sequences, namely the algebraic limit theorem and the order limit theorem.
-
Limit of Sequence
- College aantekeningen • 2 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Give an epsilon proof for the limit of a sequence, where in more detail the partial sum of a series and its convergence is explained and tested with the p-series test. Then, introduce the Cauchy sequence and the monotone convergence theorem.
-
Consequences of Axiom of Completeness
- College aantekeningen • 1 pagina's • 2023 Nieuw
-
Ook in voordeelbundel
-
- €9,24
- + meer info
Explain the proof for the nested interval property, and also the proofs for the Archimedean Property, which is split into two parts.
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