Eivind Dahl
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 Apr25 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. Apr9 comment How to “grok all the major pieces” of math +1 for category theory. Apr9 comment How can there be alternatives for the foundations of mathematics? Interesting! I've been hoping you could get around it somehow. Apr9 revised How can there be alternatives for the foundations of mathematics? added 12 characters in body Apr9 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. Apr9 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 Apr9 answered How can there be alternatives for the foundations of mathematics? Apr8 awarded Nice Answer Apr8 answered Intuition behind Matrix Multiplication Apr7 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 Apr7 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. Apr6 awarded Commentator Apr6 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. Apr6 revised Why is one “$\infty$” number enough for complex numbers? added 11 characters in body Apr6 answered Why is one “$\infty$” number enough for complex numbers? Apr3 comment Is it ever true that $\Omega^n(\bigvee_I X)\simeq\bigvee_I\Omega^n X$? @Ryan Sounds good to me. Thank you! Apr3 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 :) Apr3 awarded Scholar Apr3 accepted Two definitions of exactness Apr3 asked Two definitions of exactness