Johannes Kloos
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 Dec 29 reviewed Approve How can a Kirby diagram fail to determine a handle decomposition? Dec 27 reviewed Approve The general solution of $x^a = a^x$ for real $a >0$ Dec 27 reviewed Approve Definition of exact sequence Dec 22 comment Does there exist a neighborhood around a real number on the real line whose complement is finite? As for existence: The topological space being defined is given as the space where the closed sets are the finite sets and the whole space, or equivalently, the open sets are the co-finite sets and the empty set. This is a topology: - The empty set is finite, hence closed, and the whole space has finite complement. - If you intersect arbitrarily many finite sets, the result is still finite. Equivalently, taking the union of arbitrarily many co-finite sets gives you a co-finite set. - The union of two finite sets is finite, and hence, the intersection of two co-finite sets is co-finite. Dec 22 comment Combinatorial argument for an identity Hi, two things: 1. What have you tried so far? Have you noticed the connection to "$x_1 + \ldots + x_n \le n$"? 2. The notation "${}^n C_r$" is very outdated; in general, prefer writing $\binom{n}{r}$. Dec 21 reviewed Approve sequences-and-series tag wiki excerpt Dec 12 reviewed Approve Problem using the AM-GM inequality Dec 12 reviewed Approve analysis tag wiki Nov 24 reviewed Approve Forecasting multiple data sets - mean and standard deviation Nov 22 reviewed Approve How many integers between $10000$ and $99999$, inclusive, are divisible by $3$ or $5$ or $7?$ Nov 22 reviewed Approve Determine if point is in the 2D square/triangle Nov 21 reviewed Approve Determine the value of $x$ that is for $x^3-6x+7=0$ is false such that $x\in\mathbb{R}$ Nov 17 reviewed Approve Range of Influence of the Wave Equation? Nov 14 reviewed Leave Open Lie algebra of the invertible morphisms of a Lie algebra. Nov 14 reviewed Leave Open Why is the Fourier transform self-inverse? Nov 14 reviewed Approve All the spaces which are Hausdorff and semi metric spaces, are necesarily metric spaces? Nov 14 reviewed Approve How do you calculate the wife's age? Nov 14 reviewed Approve The probability that $n$ items out of $m$ selected turn out to be of a particular kind Nov 14 comment What is $dx$ in integration? @Aerovistae: The $\Delta x$ describes the difference between consecutive values of $x$. Jun 14 awarded Good Answer