Class 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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Institution
University Of North Carolina - Chapel Hill
Course
Math 521 (MATH521)
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Document information
- Uploaded on
- June 7, 2023
- Number of pages
- 3
- Written in
- 2022/2023
- Type
- Class 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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