HelmutKnaust at 14:15, 15 October 2014

2014-10-15T14:15:27Z

HelmutKnaust: 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..."

2014-10-15T14:13:52Z

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..."

New page

'''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 $A=B\ \Leftrightarrow\ (A\subseteq B)\wedge (B\subseteq A)$.

@@ Line 13: / Line 13: @@
 '''Problem 25.''' Find all limit points of the set
-\[\left\{\frac{1}{m}+\frac{1}{n}\ |\ m,n\in\mathbb{N}\right\}\]
+\[\left\{\frac{1}{m}+\frac{1}{n}\ :\ m,n\in\mathbb{N}\right\}\]
 Remember that $A=B\  \Leftrightarrow\  (A\subseteq B)\wedge (B\subseteq A)$.

CRN 11982: HW 5 - Revision history

HelmutKnaust at 14:15, 15 October 2014

HelmutKnaust: 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..."