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In reference to your point, In particular, has copy-paste of mathematics been implemented so that it may be used without disadvantages
I don't know the particulars of what you cite, but the accsupp package allows different things to be displayed in a PDF versus what shows up in a copy paste.
R...
Rote learning is a memorization technique based on repetition. The idea is that one will be able to quickly recall the meaning of the material the more one repeats it. Some of the alternatives to rote learning include meaningful learning, associative learning, and active learning.
== Versus critical thinking ==
Rote methods are routinely used when fast memorization is required, such as learning one's lines in a play or memorizing a telephone number.
Rote learning is widely used in the mastery of foundational knowledge. Examples of school topics where rote learning is frequently used include phonics...
I want to check if the following integrals converge or diverge.
$\displaystyle{\int_1^{+\infty}\frac{(\ln t)^{\beta}}{t^{\alpha}}\, dt, \alpha ,\beta\in \mathbb{R}}$
$\displaystyle{\int_0^{+\infty}\frac{t\ln t}{(1-t^2)^2}\, dt}$
$\displaystyle{\int_1^{+\infty}\frac{|\sin t|}{t}\, dt}$
$\disp...
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So this is proposition $4.8$ in Lorenzini's "An invitation to arithmetic geometry":
Let $A$ be a domain, integrally closed, in its field of fractions $K$. Let $L/K$ be a separable extension of degree $n$. Let $\{ e_1, ..., e_n \} \subset B$ be a basis for $L$ over $K$ where $B$ is the integral cl...
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