975 reputation
512
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location Oslo, Norway
age 26
visits member for 4 years, 3 months
seen 12 hours ago

Master student in algebraic topology at the University of Oslo.


Apr
25
comment A question on differentiability of the inverse of strictly monotonically increasing functions
Yup, the answers down below cover it. Just to be sure you're not missing out on anything; the inverse $f^{-1}$ of a real to real function can aquired from the graph of $f$ by just flipping the xy plane along the diagonal. If you haven't already you might find it worthwhile to connect the algebraic picture below with this geometric picture.
Apr
9
comment How to “grok all the major pieces” of math
+1 for category theory.
Apr
9
comment How can there be alternatives for the foundations of mathematics?
Interesting! I've been hoping you could get around it somehow.
Apr
9
revised How can there be alternatives for the foundations of mathematics?
added 12 characters in body
Apr
9
comment How can there be alternatives for the foundations of mathematics?
You talking about the appendix which I removed? Sheaf topoi are Grothendieck topoi. I'm not entirely sure how this all ties together. But it's a huge and interesting field no less.
Apr
9
revised How can there be alternatives for the foundations of mathematics?
No point to have that unfinished appendix hanging around.; added 608 characters in body
Apr
9
answered How can there be alternatives for the foundations of mathematics?
Apr
8
awarded  Nice Answer
Apr
8
answered Intuition behind Matrix Multiplication
Apr
7
comment Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
Oh gee of course! :p
Apr
7
comment Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
Bravo, bravo! I quite like it. I want to read about "because the equality holds for infinitely many values of x (and we are working over Z...)". Do you have a reference? It's probably in my algebra book, and it does make sense.
Apr
6
awarded  Commentator
Apr
6
comment Same symbol “$\partial$” - different things ( the boundary $\partial A$ / partial derivative $\frac{\partial f}{\partial x}$)?
The integral $\int_a^b f(x) dx$ of a map $f:[a,b]\to\mathbb{R}$ is the same thing as the difference $F(b)-F(a)$ where $F$ is the antiderivative of $f$. Notice that $a,b$ are the boundary points of $[a,b]$, and that $f=F'$. This connection between integration over a cell and its boundary gives us Stokes' theorem. When integration happens in several dimensions, we need the partial derivatives in there. I'm not sure about if this choice of notation was intentional.
Apr
6
revised Why is one “$\infty$” number enough for complex numbers?
added 11 characters in body
Apr
6
answered Why is one “$\infty$” number enough for complex numbers?
Apr
3
comment Is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$?
@Ryan Sounds good to me. Thank you!
Apr
3
comment Two definitions of exactness
Thanks a lot! I suspected it would have something to do with building the limit from products and equalizers. That fact will probably prove a good exercise :)
Apr
3
awarded  Scholar
Apr
3
accepted Two definitions of exactness
Apr
3
asked Two definitions of exactness