User:Spin

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ca	Aquest usuari té el català com a llengua materna.

es	Este usuario tiene el español como lengua materna.

fr-4

Cet utilisateur parle français à un niveau comparable à la langue maternelle.

en-3

This user is able to contribute with an advanced level of English.

qya-1

Yuhtaro sina ná Þundo hanyo quenyanen.

qu-1

Kay ruwaq wamaq Runa Simi yachanawan ayninakunman.

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Wikipedia:Babel

$e^{i \pi} \,\;$

This user is a mathematician.

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Wikipedia:Babel

C-3

This user is an advanced C user.

c++-3

This user is an advanced C++ programmer.

-4	This user is an expert LaTeX user.

HTML-3

This user is an advanced HTML user.

js-3

This user is an advanced JavaScript coder.

css-3

This user is an advanced Cascading Style Sheets user.

java-3

This user is an advanced Java programmer.

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In mathematics, a Grothendieck universe is a set with the following properties:

If x ∈ U and if y ∈ x, then y ∈ U.
If x,y ∈ U, then {x,y} ∈ U.
If x ∈ U, then P(x) ∈ U. (P(x) is the power set of x.)
If $\{x_\alpha\}_{\alpha\in I}$ is a family of elements of U, and if I ∈U, then the union $\cup_{\alpha\in I} x_\alpha$ is an element of U.

A Grothendieck universe is meant to provide a set in which all of mathematics can be performed. (In fact, it provides a model for set theory.) As an example, we will prove an easy proposition...