Alex Nelson
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 Jan25 comment For what values is my integral diverging or converging? You ought to simplify $\alpha_{1}/2$ as 1 everywhere...it cleans things up a bit... Jan25 comment Simplify the sum $\sum_{k=1}^{\infty} (\frac{1}{2})^kk$ What's $\sum_{n=0}x^{n}$ converge to? What's its derivative? Dec8 comment Is it possible to create division via Set Theory? You can formally construct the integers with an equivalence relationship atop the natural numbers, then construct the rationals using the integers you've just constructed. Sep29 comment Geometric Interpretation of QFT Scattering Integrals @Dave, the "generalization to $n$ dimensions" section discusses $\int_{\mathbf{R}^n} \delta(g(\mathbf{x}))\, f(g(\mathbf{x}))\, |\det g'(\mathbf{x})|\, d\mathbf{x} = \int_{g(\mathbf{R}^n)} \delta(\mathbf{u}) f(\mathbf{u})\,d\mathbf{u}$ and $\int_{\mathbf{R}^n} f(\mathbf{x}) \, \delta(g(\mathbf{x})) \, d\mathbf{x} = \int_{g^{-1}(0)}\frac{f(\mathbf{x})}{|\mathbf{\nabla}g|}\,d\sigma(\mathbf{x})$ Sep26 comment Riemann Zeta of 1/2 $\zeta(\frac{1}{2})$ For your first equation, why is it true for $x>1$, but you conclude a result for $x>0$? [I can't immediately see it, so even if you say something like "Equation x justifies it" would be appreciated :)] Aug14 comment Is Category Theory geometric? This book review claims "in this book his principal objective is to establish the claim that category theory is a generalization of Felix Klein's Erlangen program." So, what the author means by "geometrical" should probably be understood in that light... Jul27 comment How to I write $\frac{7^{2n}}{4^{3n}}$ as a geometric series? Wait, you are trying to consider $\sum(7/4)^{2n}$? That would diverge badly... Jul20 comment An English question for a logical term Well, be fair, the three google results are: this thread, the other thread you linked to, and a paper which has the exact phrase "...depend only on the presence, in the tuple, of implications...". It looks like no one uses the term "tuple of implications", per se. Jun17 comment How to compute this integral involving sech? I think you might want to consider the stationary phase approximation...or method of steepest descent, whichever (I always get them confused!). Jun17 comment How to compute this integral involving sech? What have you tried? (And is $\epsilon$ "small and positive"?) Jun17 comment Question on $\mathfrak{sl}(2,\mathbb R)$ @PeterFranek, could you remind me why it's not a group? I thought it was a subgroup (since it has the identity element and the Baker-Campbell-Hausdorff formula suggests it is closed under multiplication, right?) but rarely is it the full group...am I mistaken? Jun8 comment Intuition behind the definition of a derivative by Lang Maybe it's because I'm drunk, but isn't the $\lambda y$ term merely the linear term (i.e., derivative) and $\varphi(y)$ the "bonus parts which vanish in the appropriate limit"? Just as if for a usual function in calculus 101 we would Taylor expand $f(x+h)=f(x)+f'(x)h+g(h)$ where $g(h)\sim o(h^{2})$. The derivative would naturally be the linear (first) term...well, the coefficient to $h$... May11 comment What's the term for a “physical vector space”? @RobertIsrael perhaps use the "accountant's trick" and let negative fruit be a deficit owed to someone, and fractional fruit be a fraction of a fruit? (It works in Sraffian economics!) May3 comment How would you evaluate $I:=\int_ {0}^{\infty} \frac {\cos(ax)} {(x^2 + b^2)^n} \ \mathrm{d}x$? Consider the real part of the integral $\int(x^2+b^2)^{-n}\exp(iax)\,\mathrm{d}x$ might help... Apr22 comment What's the name of this category Isn't it isomorphic to the category $C_{A\times B}$? Apr20 comment Link between a topological space and a manifold The topology is the collection of open sets of the space (by definition, a member of the topology is called an "open set"). But when a manifold "locally looks Euclidean", you're talking about charts...the image of a chart is itself an open set in the manifold, which requires a topology to talk about... Apr20 comment Why the $\zeta$ letter is like this? @Goos, the difference is really negligible. Once you get one method of writing a zeta, it's not terribly difficult to deform the orthography into the one you desire. But starting with some zeta, I found, has been the hard part (for me anyways). Apr20 comment Why the $\zeta$ letter is like this? foundalis.com/lan/hw/grkhandw.htm Apr15 comment Solve $\sqrt{1+\sqrt{1-4x^2}}=x\left( 1+\sqrt{1+\sqrt{1+2\sqrt{1-4x^2}}}\right).$ Perhaps set $u=\sqrt{1-4x^{2}}$, so $x = \sqrt{1-u^{2}}/2$ and the problem becomes $2=\sqrt{1-u}(1+\sqrt{1+\sqrt{1+2u}})$...? Apr11 comment Evaluate $\int_{0}^{\pi/4}\frac{6 - 6\sin^{2}(x)}{2\cos^2(x)} \mathrm{d}x$ So...what have you attempted so far?