given that $P=(x,x,x)$ and $Q=(y,3y,-1)$ are two lines in $\mathbb{R}^3$ then I need to express in matrix form $\|AX-b\|^2$ to find the distance between $P$ and $Q$. I need to find two points on this line which are closest to each other. I tried like: $\begin{bmatrix}1&1&1\\ 3&1&0\end{bmatrix}\b...

I keep hearing people say that Bourbaki is difficult for most undergraduates but I still don't understand why. Surely if it starts from definitions/axioms then practically anyone should be able to understand it, let alone just graduate/advanced undergraduates. I didn't have any trouble reading Eu...

Which notation ($\subset$ or $\subseteq$) was preferred by Bourbaki for set inclusion (not proper)? A side question: Was the notation for subset one of the many notations invented by Bourbaki?

I have taken a first course in general topology (first four chapters of Munkres's Topology), now I want to learn more general topology. I heard Topology by Bourbaki is very good but it also needs lots of set theory. So my question is: Is the first chapter of Munkres on set theory enough to st...

So my understanding is that a while back a group of mostly French mathematicians, under the pseudonym Bourbaki, wrote a somewhat austerely written series titled "Elements of Mathematic(s)" covering a large swath of the discipline, starting from the very ground up with an axiomatic set theory. The...

What is the formal Dirichlet-Bourbaki definition of a function? I have come across this in this essay: http://www.k-12prep.math.ttu.edu/journal/contentknowledge/meel01/article.pdf on page 1. I know what a function is and I can write down a definition. What I would like to know is what the the d...

As I was preparing a short lecture (for amateurs) on the mathematics of the '900, I realized that this year marks the 70-th anniversary of the founding of the Bourbaki group. I remember that Bourbaki has been important in my formation (in the years 1970-80), when it was considered as a "school" ...

This is Exercise III.2.8 of Bourbaki's Theory of Sets. An ordered set $E$ is said to be ramified if, for each pair of elements $x,y$ of $E$ such that $x<y$, there exists $z>x$ such that $y$ and $z$ are not comparable. $E$ is said to be completely ramified if it is ramified and has no maximal ele...

Can the Bourbaki series be used profitably by undergraduates and high school students?Are we the target audience? I came across the N.Bourbaki texts while surfing the internet(I have not had the opportunity to access them though) and was a bit amazed by the Wikipedia article suggesting they did m...

I just opened vol.1 of the Bourbaki treatise to take a look at how they define mathematical structure. I was amazed by its sheer complexity. Can you recommend an introductory text that wouldn't require as much effort to understand? Also, a few related soft questions: 1) Is category theory more g...

In the book Set theory, Chapter 3 N.Bourbaki, I would like to understand how Bourbaki proves ZL. I wrote the proof. It uses Zermelo's principle (which is okay since they are equivalent), so I tried to understand how Zermelo's principle is proved but I can't find any occurrence of the axiom of cho...

On page 5 of the following write up, the author asks why the Bourbaki did not notice that their system of Zermelo set theory with AC was inadequate for existing mathematics. Throughout the rest of the discussion, the author asserts that the Bourbaki group never acknowledged Godel's results on inc...

I'm reading the first book by Bourbaki (set theory) and he introduces this logical symbol $\tau$ to later define the quantifiers with it. It is such that if $A$ is an assembly possibly contianing $x$ (term, variable?), then $\tau_xA$ does not contain it. Is there a reference to this symbol $\...

I know Nicolas Bourbaki "is the pseudonym of a group of (mainly) French mathematicians who publish an authoritative account of contemporary mathematics." But what characterizes "Bourbaki's style in mathematics"?

This is Exercise I.11.4 of Bourbaki's General Topology. Let $X$ be a connected space. a) Let $A$ be a connected subset of $X$, $B$ a subset of $\complement A$ which is both open and closed in $\complement A$. Show that $A\cup B$ is connected. b) Let $A$ be a connected subset of $X$ and $B$ a ...

In Bourbaki, Algebra I, chapter I, §5 "Groups operating on a set" paragraph 1, Bourbaki defines the operation of a group $G$ on a set $E$ as a morphism $\alpha \in G\mapsto f_\alpha \in S(E)$ ($S(E)$ is the group of permutations of $E$). Then he defines a faithfull operation asking the morphisme ...

I am now looking theorem 2 in paragraph 4.1 of: Bourbaki. "Elements of Mathematics General Topology. Part 1". THEOREM 2. Every continuous mapping $f$ of a compact space $X$ into a uniform space $X'$ is uniformly continuous. Now I realize that I don't understand the proof. Could you present me...