(Un-)Countable union of open sets - Mathematics Stack Exchange
$\begingroup$ A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that.
Prove that the sequence (1+1/n)^n is convergent [duplicate]
Mar 27, 2019 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Calculate the cohomology group of $U(n)$ by spectral sequence.
May 31, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
What does the letter epsilon signify in mathematics?
Here's a not too well-known instance of the use of $\varepsilon$ in mathematics: One somewhat well-known transformation for accelerating the convergence of a sequence is the Shanks transformation (after Daniel Shanks, who is probably more well-known for …
Exactly how does the equation n (n-1)/2 determine the number of …
Apr 2, 2017 · I understand the purpose for division. Multiplication is simply repeated addition and division is simply repeated subtraction. So lets say we have 4 total items. Plugging 4 into the equation we get...
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Given a 95% confidence interval why are we using 1.96 and not 1.64?
Oct 15, 2015 · To Find a critical value for a 90% confidence level. Step 1: Subtract the confidence level from 100% to find the α level: 100% – 90% = 10%.
math history - Why do the French count so strangely?
May 15, 2013 · Similarly, 80 is also not invented, it is 4 20s, quatre-vingt. 81 is 4 20s 1, quatre-vingt-un. 90 is, 4 20s 10, quatre-vingt-dix. 91 is 4 20s 11, quatre-vignt-onze. Finally, they have a word for 100, ceut. It looks similar to roman numbers Roman number system, where you repeat the letters to combine the values. X is 10 XX is 20 and so on.
Proof a graph is bipartite if and only if it contains no odd cycles
Apr 29, 2024 · (By contradiction) (->) Suppose n is odd. Let X={ui such that i is odd} and Y={ui such that i is even} as the bipartition formed in the graph. Consider cycle C=u1 u2 u3 u4...un u1 as the cycle in G. If u1 is odd, un can not be odd because there will be no bipartite formed. Therefore, n should be even.
Do positive semidefinite matrices have to be symmetric?
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