Stack Exchange

José Carlos Santos

Porto, Portugal

http://www.fc.up.pt/mp/jcsantos/

I am a mathematician who works at the University of Porto (Portugal). My PhD, on Representation Theory, was obtained at the Université Paris — Denis Diderot, in 1996.

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Top Questions
87 votes

Unexpected examples of natural logarithm

soft-question logarithms big-list asked Jul 3 '17 at 13:07
math.stackexchange.com

35 votes

Proving $\left(1-\frac13+\frac15-\frac17+\cdots\right)^2=\frac38\left(\frac1{1^2}+\frac1{2^2}+\frac1{3^2}+\frac1{4^2}+\cdots\right)$

real-analysis sequences-and-series summation asked Oct 2 '17 at 10:17
math.stackexchange.com

22 votes

Is every matrix conjugate to its transpose in a continuous way?

linear-algebra matrices continuity asked Dec 14 '18 at 10:03
math.stackexchange.com

19 votes

Did Emanuel Lasker write a book declaring that Germany had to win World War I if civilization were to be saved?

world-war-one germany book biography asked Sep 12 '18 at 9:48
history.stackexchange.com

14 votes

Egyptian fractions with very large denominators

reference-request algorithms egyptian-fractions asked Jul 20 '18 at 9:34
math.stackexchange.com

14 votes

Constructing the reals from the integers

reference-request real-numbers asked Aug 25 '17 at 14:41
math.stackexchange.com

14 votes

Was the insanity of kings used as an argument against monarchy?

monarchy republic asked Apr 9 at 10:09
history.stackexchange.com

12 votes

Why those who dislike the fact that the reals are uncountable always attack Cantor's diagonal proof?

soft-question infinity asked Aug 19 '17 at 14:50
math.stackexchange.com

11 votes

Are there any cases of rewarding an enemy commander for sparing a city from looting?

warfare loot asked Feb 6 '18 at 23:32
history.stackexchange.com

11 votes

Is there evidence that the annual pilgrimage to Mecca facilitated cultural exchanges?

middle-ages cultural-history islamic-history asked Jul 12 '18 at 12:31
history.stackexchange.com

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Top Answers
115
Why not include as a requirement that all functions must be continuous to be differentiable?
math.stackexchange.com

81
Can a binary operation have an identity element when it is not associative and commutative?
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78
Does an increasing sequence of reals converge if the difference of consecutive terms approaches zero?
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65
Unsolved Problems (Not Independent of ZFC) due to Lack of Computational Power
math.stackexchange.com

56
Why a $20$ digit number starting with eleven $1$'s cannot be a perfect square?
math.stackexchange.com

56
False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
math.stackexchange.com

47
How many times do you have to use L'Hôpital's rule?
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46
How are the known digits of $\pi$ guaranteed?
math.stackexchange.com

45
Can we use symmetry rules in improper integrals?
math.stackexchange.com

44
How to determine if a set of five $2\times2$ matrices is independent
math.stackexchange.com

44
Why is the notion of analytic function so important?
math.stackexchange.com

41
If derivative of $f$ is continuous, then $f$ is continuous.
math.stackexchange.com

41
Problem with estimating a sequence with intuition
math.stackexchange.com

39
Understandable questions which are hard for non-mathematicians but easy for mathematicians
math.stackexchange.com

39
Non abelian group which contains no abelian subgroup
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37
Can the product of three complex numbers ever be real?
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36
Integration of secant
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35
Simple Calculus view on Fermat's Last Theorem
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35
Finding the 10th root of a matrix
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35
How could $\varnothing$ be unique if it could be vacuously false?
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34
Sets that are both Sum-free and Product-free
math.stackexchange.com

33
If I don't have a computer at hand (or an app), how can I know that $1637$ is prime?
math.stackexchange.com

32
Why does Zorn's Lemma fail to produce a largest group?
math.stackexchange.com

32
Are these square matrices always diagonalisable?
math.stackexchange.com

32
What is the context for Napoleon's quote “[the Austrians] did not know the value of five minutes”?
history.stackexchange.com

31
General request for a book on mathematical history, for a VERY advanced reader.
math.stackexchange.com

31
Proof that a strictly decreasing sequence of nested intervals boils down to a single point.
math.stackexchange.com

31
Cross product in higher dimensions
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29
Representing zero as a rational number
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29
which is Greater $31^{11}$ or $17^{14}$
math.stackexchange.com

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