CRN 11982: HW 5
From Classes
(Difference between revisions)
HelmutKnaust (Talk | contribs) (Created page with " '''Problem 21.''' Exercise 3.2.2 (a-c) '''Problem 22.''' Given a set $X$ of real numbers, let $L$ be the set of all limit points of $X$. Show that $L$ is closed. '''Probl...") |
HelmutKnaust (Talk | contribs) |
||
| Line 13: | Line 13: | ||
'''Problem 25.''' Find all limit points of the set | '''Problem 25.''' Find all limit points of the set | ||
| − | \[\left\{\frac{1}{m}+\frac{1}{n}\ | + | \[\left\{\frac{1}{m}+\frac{1}{n}\ :\ m,n\in\mathbb{N}\right\}\] |
Remember that $A=B\ \Leftrightarrow\ (A\subseteq B)\wedge (B\subseteq A)$. | Remember that $A=B\ \Leftrightarrow\ (A\subseteq B)\wedge (B\subseteq A)$. | ||
Latest revision as of 08:15, 15 October 2014
Problem 21. Exercise 3.2.2 (a-c)
Problem 22. Given a set $X$ of real numbers, let $L$ be the set of all limit points of $X$. Show that $L$ is closed.
Problem 23. Show: If $X$ is both open and closed, then $X={\mathbb R}$ or $X=\emptyset$.
Problem 24. Exercise 3.2.9 (a)
Problem 25. Find all limit points of the set
\[\left\{\frac{1}{m}+\frac{1}{n}\ :\ m,n\in\mathbb{N}\right\}\]
Remember that $A=B\ \Leftrightarrow\ (A\subseteq B)\wedge (B\subseteq A)$.
