It is currently Mon Oct 23, 2017 6:52 am


All times are UTC [ DST ]




Post new topic Reply to topic  [ 1 post ] 
Author Message
PostPosted: Sat Jul 22, 2017 9:33 am 

Joined: Sat Nov 14, 2015 6:32 am
Posts: 127
Location: Melbourne, Australia
For which positive integers $n$ does there exist expression

$$\mathbb{R}^2 = \bigcup_{m=1}^{\infty} A_m$$

Attachment:
disks.jpg
disks.jpg [ 35.48 KiB | Viewed 90 times ] disks.jpg [ 35.48 KiB | Viewed 90 times ]


where each $A_m$ is a disk of radius $1$ such that each point $x \in \mathbb{R}^2$ belongs to either the boundary of some $A_m$ or to precisely $n$ interiors of the sets $A_1$ , $A_2$ , $\dots$ ?

_________________
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$


Top
Offline Profile  
Reply with quote  

Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 1 post ] 

All times are UTC [ DST ]


Mathimatikoi Online

Users browsing this forum: No registered users and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group Color scheme created with Colorize It.
Theme created StylerBB.net