by Agnishom Chattopadhyay
Last Updated October 20, 2019 05:20 AM

Suppose that $F_0$ is the collection of all the finite sets of $\mathbb{N}$ and $G_0$ is the collection of all the co-finite sets of $\mathbb{N}$.

Define $F_{i+1}$ to be $\{f \cup g \mid f \in F_i, g \in G_i\}$ and $G_{i+1}$ to be $\{f \cap g \mid f \in F_i, g \in G_i\}$ for all $i \in \mathbb{N}$.

Does there exist $i$ such that $F_i = G_i = F_{i+1} = G_{i+1} = \cdots$?

With some elementary calculations, the answer appears to be not. However, the calculations seem to get messy very soon.

My interest in this problem is to find an efficient data structure for subsets of an infinite domain (possibly $\mathbb{N}$) expresssed in terms of boolean combinations of finite sets.

Updated February 21, 2017 03:20 AM

Updated November 26, 2017 19:20 PM

- Serverfault Query
- Superuser Query
- Ubuntu Query
- Webapps Query
- Webmasters Query
- Programmers Query
- Dba Query
- Drupal Query
- Wordpress Query
- Magento Query
- Joomla Query
- Android Query
- Apple Query
- Game Query
- Gaming Query
- Blender Query
- Ux Query
- Cooking Query
- Photo Query
- Stats Query
- Math Query
- Diy Query
- Gis Query
- Tex Query
- Meta Query
- Electronics Query
- Stackoverflow Query
- Bitcoin Query
- Ethereum Query