## What are Dataframes?

### Understand dataframes from a non-example

Motivation The books that I read in the past didn't explain what a dataframe meant. Definition Dataframe : A table of data in which the values of each observed variable is contained in the same column. Counterexample I've difficulty in reading long lines of text like the above definition, so let's illustrate this definition with a counterexample. We have carried out repeated experiments with four types of things and obtaine some data. [Read More]

## Ultrafilters Are Maximal

Ultra filter : A filer $\mathcal{F}$ containing either $Y$ or $Y^\complement$ for any $Y \subseteq X$. Two days ago, I spent an afternoon to understand Dudley's proof of this little result. A filter is contained in some ultrafilter. A filter is an ultrafilter iff it's maximal. At the first glance, I didn't even understand the organisation of the proof! I'm going to rephrase it for future reference. only if: let $\mathcal{F}$ be an ultrafilter contained in another filter $\mathcal{G}$. [Read More]