Lecture notes
Consequences from Axiom of Completeness Continued.
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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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Connected book
Understanding Analysis
- 2012
- 9780387215068
- Unknown
Written for
- Institution
- University Of North Carolina - Chapel Hill
- Module
- Math 521 (MATH521)
All documents for this subject (11)
Document information
- Uploaded on
- June 7, 2023
- Number of pages
- 3
- Written in
- 2022/2023
- Type
- Lecture notes
- Professor(s)
- Idris assani
- Contains
- All classes
Subjects
-
axiom of completeness
-
sequences
-
algebraic limit theorem
-
order limit theorem
-
dense
-
contradition
-
proofs
-
calculus
-
advanced calculus
-
desntiy of rational numbers
-
existence of square root of 2
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