20,616 reputation
13059
bio website facebook.com/paterz1
location Montreal, Canada
age 23
visits member for 3 years, 4 months
seen 4 hours ago

I finished my undergraduate studies in mathematics at University of Montreal. I am doing my Ph.D at the Berlin Mathematical School in algebraic geometry. My current interests, besides algebraic geometry, are number theory, analysis, topology, measure theory, representation theory and commutative algebra.


7h
comment Why we use dummy variables in integral?
@egreg : I know, but I said we ''can'' not use them (now I need to switch my '' of position to put emphasis on something else...) I actually expected your comment somehow.
12h
comment Why we use dummy variables in integral?
Note that in measure theory, we can ''not'' use them. We use a measure $\mu$ (in your case the measure would be ''$dx$'', i.e. the Lebesgue measure, even though you probably know Riemann integration... doesn't matter) and we write $\int f \, d\mu$.
13h
comment Convergence of $\sum_{n=1}^{\infty}\frac{1}{n^\alpha}$
This is a comment, not an answer. You should have put it under the comments sections of the question. Feel free to edit.
1d
comment Why $\int {dx \over x \sqrt{x+3}} \neq \int {2u\cdot du \over (u^2-3)u} \rvert_{u=\sqrt{x+3}} $?
The integral of $\frac 1u$ is $\log |u|$, but the integral of $\frac 1{u^2-3}$ is not $\log|u^2-3|$. Otherwise we wouldn't bother and write $$ \int f(x) \, dx = \int \frac 1{1/f(x)} \, dx = \log|1/f(x)| + C $$ which is of course false!
1d
comment Why $\int {dx \over x \sqrt{x+3}} \neq \int {2u\cdot du \over (u^2-3)u} \rvert_{u=\sqrt{x+3}} $?
@Matt : Oh, sorry I didn't see that $u$ in the denominator (why is it there in the first place?... :( ) The thing we keep repeating students during integration courses is that using computers to verify indefinite integrals can be confusing ; the results will all be equal up to a constant, and sometimes, up to a constant, functions can have a veeeeeeeery different appeareance.
1d
comment Why $\int {dx \over x \sqrt{x+3}} \neq \int {2u\cdot du \over (u^2-3)u} \rvert_{u=\sqrt{x+3}} $?
P.S. : You wrote $u = x+3$ in your comment... I assume you meant $u = \sqrt{x+3}$, but just in case, the substitution $u=x+3$ would've given you the integral $$ \int \frac{du}{(u-3)\sqrt u} $$
1d
revised Why $\int {dx \over x \sqrt{x+3}} \neq \int {2u\cdot du \over (u^2-3)u} \rvert_{u=\sqrt{x+3}} $?
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1d
comment Why $\int {dx \over x \sqrt{x+3}} \neq \int {2u\cdot du \over (u^2-3)u} \rvert_{u=\sqrt{x+3}} $?
@Matt : Did you notice my result for the substitution $u = \sqrt{x+3}$ is not the same as yours?
1d
answered Why $\int {dx \over x \sqrt{x+3}} \neq \int {2u\cdot du \over (u^2-3)u} \rvert_{u=\sqrt{x+3}} $?
Sep
19
comment does uncorrelation imply mean independence?
@Did : I know, I got it the wrong way around... anyway this was a bad example ; I removed it. I didn't do these things in a long time, memory is working at the moment.
Sep
19
comment does uncorrelation imply mean independence?
I added an example which fits the context of the OP. @user119758 take a look!
Sep
19
revised does uncorrelation imply mean independence?
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Sep
19
comment does uncorrelation imply mean independence?
@user119758 : Do you know anything about the variables $\epsilon_i$ and $\epsilon_j$ other than the covariance condition and expectation conditions? Otherwise I'm pretty much convinced there are counter-examples.
Sep
19
answered does uncorrelation imply mean independence?
Sep
18
answered Matrix equation xA=x
Sep
18
comment Matrix equation xA=x
What do you mean $xA = x$? Do dimensions even agree? If $A$ is an $m \times n$ matrix, then they agree if and only if $m = n = 1$, which is kind of boring. And um, the linear system $Ax=x$ has techniques to be solved yes, but it is not a "trivial" system in the mathematical sense.
Sep
16
comment What will be the multiplicative inverse of square root of 5 with respect to a natural number $M$?
It depends how you define the square root of $5$, i.e. in which ring. There are rings of the form $\mathbb Z / n \mathbb Z$ in which the equation $x^2 = 5$ has a solution. For instance, $4^2 \equiv 5 \pmod{11}$.
Sep
15
revised Is the reverse of the second fundamental theorem of calculus always true?
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Sep
15
comment Is the reverse of the second fundamental theorem of calculus always true?
@icurays1 : Sure, let's say I assumed continuous.
Sep
15
comment How to write a formal proof of the statement: For all integers n, if n is a multiple of 5 then 3n is a multiple of 5.
What does "$5k \Rightarrow n$" even mean?