on 18-May-2018 (Fri)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

The best known fields are the field of rational numbers and the field of real numbers.

the relative complement of A in B is the set of elements in B but not in A .

The relative complement of \({\displaystyle B\cap A^{\complement }=B\setminus A}\)

If \({\mathcal {F}}\,\) is the Borel σ-algebra on the set of real numbers, then there is a unique probability measure on \({\mathcal {F}}\,\) for any cdf, and vice versa.

Segundo Platão/Sócrates, todo o ato intelectual só pode ter lugar na alma

Tendo construído os corpos de cada um deles – sete ao todo –, o deus estabeleceu-os nas órbitas que o percurso do Outro seguia, em número de sete delas: na primeira a Lua, à volta da Terra; na segunda o Sol, por cima da Terra 125 ; a Estrela da Manhã 126 e o astro que dizem ser consagrado a Hermes 127 na rota circular 128 que tem a mesma velocidade que o Sol, ainda que lhes tenha cabido em sorte um ímpeto contrário ao dele

Quanto à Terra, o nosso sustento, a qual roda 136 em torno do eixo que atravessa o universo, foi estabelecida como guardiã e produtora da noite e do dia; ela que é a primeira e a mais velha das divindades geradas dentro do céu

De Geia e Urano foram gerados Oceano e Tétis, seus filhos, e destes foram gerados Fórcis, Cronos e Reia, e todos aqueles que os seguiram; de Cronos e de Reia foram gerados Zeus e Hera e todos aqueles que, segundo a tradição, sabemos serem seus irmãos, e ainda outros descendentes destes foram gerados.

formai e engendrai seres-vivos, fazei-os crescer, providenciando- lhes o alimento, e, quando perecerem, recebei-os outra vez.

Uma vez acalmados, gera-se o sossego, e, uma vez gerado um sossego profundo, abate-se um sono com poucos sonhos; mas quando restam alguns movimentos fortes, conforme a sua natureza e os locais onde ficam, produzem no interior simulacros que se assemelham, quanto à natureza e ao número, ao exterior e que serão recordados ao acordar.

You should only commit code when it’s completed.

Resist the temptation to commit something that you “think” is completed. Test it thoroughly to make sure it really is completed and has no side effects

writing commit messages with the imperative, present tense to be consistent with generated messages from commands like git merge.

The body of your commit message should provide motivation to and difference of the commit.

Branches are the perfect tool to help you avoid mixing up different lines of development

Branches

In contrast to Borel sets, an example of a non-measurable set cannot be exhibited, though its existence can be proved.

The raison d'être of the measure-theoretic treatment of probability is that it unifies the discrete and the continuous cases, and makes the difference a question of which measure is used.

to study Brownian motion, probability is defined on a space of functions.

measure-theoretic treatment also allows us to work on probabilities outside \(\mathbb {R} ^{n}\), as in the theory of stochastic processes .

Weak convergence is also called convergence in distribution. Most common shorthand notation: \({\displaystyle \displaystyle X_{n}\,{\xrightarrow {\mathcal {D}}}\,X}\)

The sequence of random variables \(X_{1},X_{2},\dots \,\) is said to converge towards the random variable \(X\,\) in probability if \(\lim _{n\rightarrow \infty }P\left(\left|X_{n}-X\right|\geq \varepsilon \right)=0\) for every ε > 0. Most common shorthand notation: \({\displaystyle \displaystyle X_{n}\,{\xrightarrow {P}}\,X}\)

The sequence of random variables \(X_{1},X_{2},\dots \,\) is said to converge towards the random variable \(X\,\) strongly if \(P(\lim _{n\rightarrow \infty }X_{n}=X)=1\). Strong convergence is also known as almost sure convergence. Most common shorthand notation: \({\displaystyle \displaystyle X_{n}\,{\xrightarrow {\mathrm {a.s.} }}\,X}\)

To check, run vim --version and see if +clipboard exists.

echo $SHELL # displays the shell you're using

Treat the data (and its format) as immutable.

Therefore, by default, the data folder is included in the .gitignore file.

When we use notebooks in our work, we often subdivide the notebooks folder.

Notebooks are for exploration and communication

Follow a naming convention that shows the owner and the order the analysis was done in.

1. Refactor the good parts. Don't write code to do the same task in multiple notebooks. If it's a data preprocessing task, put it in the pipeline at src/data/make_dataset.py and load data from data/interim. If it's useful utility code, refactor it to src.

Now by default we turn the project into a Python package (see the setup.py file). You can import your code and use it in notebooks with a cell like the following:

We prefer make for managing steps that depend on each other, especially the long-running ones.

The first step in reproducing an analysis is always reproducing the computational environment it was run in.

By listing all of your requirements in the repository (we include a requirements.txt file) you can easily track the packages needed to recreate the analysis.

Store your secrets and config variables in a special file

Create a .env file in the project root folder. Thanks to the .gitignore, this file should never get committed into the version control repository.

but setting the default editor and then using

 git commit - e 

might be much more comfortable.

Providing metadata is a fundamental requirement when publishing data on the Web because data publishers and data consumers may be unknown to each other.

Besides building programs, Make can be used to manage any project where some files must be updated automatically from others whenever the others change.

Make is invoked with a list of target file names to build as command-line arguments:

Make decides whether a target needs to be regenerated by comparing file modification times.

This solves the problem of avoiding the building of files which are already up to date, but it fails when a file changes but its modification time stays in the past.

Make searches the current directory for the makefile to use

The makefile language is similar to declarative programming.^{[32][33][34][35]} This class of language, in which necessary end conditions are described but the order in which actions are to be taken is not important

Make allows us to specify what depends on what and how to update things that are out of date.