Existence of open sets $U, V$ of matrices such that for every $A \in U$ there exists $B \in V$ such that $B^4 = A$

Unable to solve $ \int \frac{x + \sqrt{2}}{x^2 + \sqrt{2} x + 1} dx $?

Modular Arithmetic in AMC 2010 10A #24

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Is this a valid proof that A = B given A ∩ B = A ∪ B?

Simple computation with the $n$-form $dz_1\wedge...\wedge dz_n$ in $\mathbb{C}^n$

Integrating $\int^2_0 xe^{x^2}dx$

Compute $\lim \limits_{n\to \infty} \frac{1}{n}\sum_{i,j=1}^n\frac{1}{\sqrt{i^2+j^2}}$

confused about a matrix problem

Simplify, equivalent for (p ∨ ¬q) ∧ (¬p ∨ ¬q)

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Fibonacci sequence and other metallic sequences emerged in the form of fractions

Why should the equality of mixed partials be "intuitively obvious"?

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