Marcel T.
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 2d awarded Yearling Mar18 comment What does it mean to have no proper non-trivial subgroup A "proper nontrivial subgroup" is a subgroup which is both a proper subgroup and a nontrivial subgroup. Mar11 revised What is the difference between $\mathbb{R}$ with the $K$ topology and $\mathbb{R}_k$? added 89 characters in body Mar11 answered What is the difference between $\mathbb{R}$ with the $K$ topology and $\mathbb{R}_k$? Feb21 comment Give a natural deduction proof of $\varphi\vdash\top$, there $\varphi$ is any formula The way I was taught, the Natural Deduction calculus had a $\top$ formation rule. That was kind of the whole use of introducing the predicate $\top$ in the first place. It might help to reference what exposition of Natural Deduction you are following. Feb21 answered Question about deduction in first order logic Feb21 suggested rejected edit on Question about deduction in first order logic Feb7 comment How come $\lambda(\mathbb{Q})= \inf\left\{\sum_{n \ge 1} \lambda([a_n,b_n)) : \mathbb{Q} \subset \bigcup_{n \ge 1} [a_n,b_n)\right\} = 0$? My intuition is game-theoretic one: I imagine a game where Player 1 has countably many points he can throw out and demand get covered, and Player 2 has $\epsilon$ much length of tape that he's allowed to cut pieces off from to tape over Player 1's challenges. Each time Player 1 demands a point get covered, Player 2 just cuts off a small portion of his tape and covers that point. At no point does Player 2 run out of tape, so in the limit, Player 2 has responded to every challenge of Player 1, and has used at most $\epsilon$ much tape. Feb7 revised Odd-degree polynomials have roots (Intermediate Value Theorem) Provided a more descriptive title Feb7 suggested approved edit on Odd-degree polynomials have roots (Intermediate Value Theorem) Feb7 comment Shortest possible unreachable shape One class of examples is to double over the snake, and then spiral it around until the ends can't be unbent. i.imgur.com/5vYPn7p.jpg I think you can at least beat Harald Hanche-Olsen's example with this approach, you might even be able to get down to 29 but I have to check more carefully. Feb4 comment How many times can a $4^{th}$ degree polynomial be equal to a prime number? This problem is weaker than showing that there exists a /single/ polynomial which takes arbitrarily many prime values. For example, the corresponding problem for quadratics was proven by Sierpenski in 1964 (that there is no bound on $n$). Feb4 comment Extremely difficult: Polynomials $f,g,h$ such that… At least for some $n$ there are no nontrivial solutions. Plug in $0$ for $x$. Then for the constant terms $a, b, c$ of $f, g, h$ we must have $(ab+bc+ca)/(a^2+b^2+c^2)$ must be equal to $(3n-3)/(9n+1)$ (if $a^2+b^2+c^2 \neq 0$). This is impossible, for example, for $n=3$. So $a^2+b^2+c^2=0$. So $a, b, c=0$. Divide everything through by $x$ and repeat. So $f, g, h=0$. Feb4 comment Model theoretic answer for having algebraic closure If you're going to iterate the process anyway, why bother applying compactness at all? Why not just add the roots in one at a time? What actual benefit does compactness have on the proof? Nov16 comment Finding $\int_0^{\pi/2} \sin x\,dx$ $\lim_{x^\circ \rightarrow 0} \frac{\sin(x^\circ )}{x^\circ}$ is most certainly $1$, by any standard. Whatever your interpretation of $x^\circ$ is, it must be as a real variable, and $\lim_{y\rightarrow 0} \frac{\sin y}{y}=1$ for any real variable $y$. Typically (e.g. by Mathematica), $x^\circ$ is interpreted via $x^\circ=x\times\frac{\pi}{180}$. Perhaps you meant to write $\lim_{x\rightarrow 0} \frac{\sin (x^\circ )}{x} = \frac{\pi}{180}$ or $\lim_{x^\circ\rightarrow 0} \frac{\sin (x^\circ )}{x} = \frac{\pi}{180}$? Either would be correct. What you have is not. Nov16 comment Intuitive understanding of the derivatives of $\sin x$ and $\cos x$ I disagree with the cynical analysis of people's calculus education. I think the reason many people answer this question poorly is because maths students are simply not familiar with degrees, as they are abandoned immediately upon entering a calculus course. And rightly so. Reasoning that an inability to answer questions about degrees is evidence of a poor calculus education is like asking European children to convert between cups and gallons, or about the Fahrenheit scale, and then concluding when they give you puzzled looks that it is "a sign of how badly the French learn arithmetic". Nov16 revised Find $\int_0^2 x^2f''(2x)dx$ given $f(2)$, $f'(2)$, and $\int_0^2 f(x)dx$ typo Nov16 revised Find $\int_0^2 x^2f''(2x)dx$ given $f(2)$, $f'(2)$, and $\int_0^2 f(x)dx$ typo Nov16 answered Find $\int_0^2 x^2f''(2x)dx$ given $f(2)$, $f'(2)$, and $\int_0^2 f(x)dx$ Nov16 comment Uncountable reals in the theory If you want the reals to really be the reals, so in particular have theory RCF, then no. RCF is not expressive enough. If you are just asking for the sake of asking, fix a countable model of ZF and a bijection between its universe and $\mathbb{R}$. Then look at the induced structure.