Top new questions this week:
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Problem: You are standing at the origin of an infinite flat earth. One quadrant of the earth is gone, leaving an infinite abyss. You have an infinite supply of unit-length zero-width planks. How far ...
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As I was going through some exercise list with limits, I found $\lim_n \sqrt[n]{1+\cos^2(n)}$. This is easy enough, since $\cos^2$ is bounded between 0 and 1, so a squeeze theorem argument lets us ...
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I want to evaluate $I=\int_{0}^{\pi /4} x^3 (\sqrt{\tan (x)} + \sqrt{\cot (x)}) dx\tag{0}$
Expressing with $\sin (x)$ and $\cos (x)$:
$$ I = \int_{0}^{\pi /4} x^3 \frac{\sqrt{2}(\sin (x) + \cos (x))}{\...
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Let $f:\mathbb{R}\to\mathbb{R}$ be continuous. For all nowhere-differentiable examples that I know of, for each $a\in\mathbb{R}$ there exist sequences $x_n\to a$ and $y_n\to a$ such that
$$\frac{f(...
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Let $X$ and $Y$ be topological spaces and let $\tau$ be a topology on the set-theoretic product $X \times Y$ such that:
The first projection $p \colon X \times Y \to X$ is continuous and open with ...
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Let $\kappa$ be a measurable cardinal. I want to show that it is still inaccessible in ZF. Using ultrapower and Los I can show that it's inaccessible in ZFC, but that doesn't seem to work here $\dots$ ...
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The greatest common divisor (gcd) of two integers $a$ and $b$ can be computed with the Euclidean Algorithm.
With the gcd known, one can compute the least common multiple (lcm) via the formula $\mathrm{...
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Greatest hits from previous weeks:
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This is one of a pair of questions trying to understand this comment on the xkcd forum contest My number is bigger than yours!. For a definition of Goodstein sequences, see this question.
Let $G(n)$ ...
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In which order do I graph transformations of functions?
The 6 function transformations are:
Vertical Shifts
Horizontal Shifts
Reflection about the x-axis
Reflection about the y-axis
Vertical ...
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This is a very simple but confusing puzzle.
A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase.
The lady gives him a $1000$ ...
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This morning, I read Wikipedia's informal definition of a limit:
Informally, a function f assigns an output $f(x)$ to every input $x$. The
function has a limit $L$ at an input $p$ if $f(x)$ is "...
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I just came across this annotation in my school's maths compendium:
The compendium is very brief and doesn't explain what this means.
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$\sin^{4}x+\cos^{4}x$
I should rewrite this expression into a new form to plot the function.
\begin{align}
& = (\sin^2x)(\sin^2x) - (\cos^2x)(\cos^2x) \\
& = (\sin^2x)^2 - (\cos^2x)^2 \\
&...
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In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
I just dipped into a book, The Drunkard's Walk - How Randomness Rules Our Lives, ...
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Can you answer these questions?
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Is there a way to conserve area of two Gausians, such that $\int f(x)dx + \int g(x)dx = \int\left[ \int f(\tau)*g(x-\tau)d\tau\right]$?
For context, I have stumbled upon a math problem in my lab and I ...
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Reading literature related to the problem of multiplicative partitions A001055 OEIS sequence (also named "factorizatio numerorum", "Oppenheim problem", "factorizations ...
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Let $A$ be a countable set of indices and for every $a\in A$ let $M_a$ be a $\sigma$-algebra on a non empty set $X_a$, generated by a family of subsets $\epsilon_a$, that is $M_a=\sigma(\epsilon_a)$. ...
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