CRN 12109: HW 1
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'''Problem 1.''' Exercise 1.3.2. | '''Problem 1.''' Exercise 1.3.2. | ||
| − | '''Problem 2.''' Exercise 1.3.3 (a)(b). | + | '''Problem 2.''' Exercise 1.3.3(a)(b). |
'''Problem 3.''' Exercise 1.4.4. | '''Problem 3.''' Exercise 1.4.4. | ||
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'''Problem 4.''' Let $A=\{x\in\mathbb{Q}\ |\ x^2\leq 5\}$. Show that A is bounded from above, but that $A$ has no maximum. | '''Problem 4.''' Let $A=\{x\in\mathbb{Q}\ |\ x^2\leq 5\}$. Show that A is bounded from above, but that $A$ has no maximum. | ||
| − | '''Problem 5.''' Show that the ''Nested Interval Property'' implies the ''Axiom of Completeness''. | + | '''Problem 5.''' Show that the ''Nested Interval Property'' together with the ''Archimedean Principle'' implies the ''Axiom of Completeness''. |
Latest revision as of 13:14, 13 September 2013
Problem 1. Exercise 1.3.2.
Problem 2. Exercise 1.3.3(a)(b).
Problem 3. Exercise 1.4.4.
Problem 4. Let $A=\{x\in\mathbb{Q}\ |\ x^2\leq 5\}$. Show that A is bounded from above, but that $A$ has no maximum.
Problem 5. Show that the Nested Interval Property together with the Archimedean Principle implies the Axiom of Completeness.
