Velvet Star Monitor

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Is there a mathematical symbol for "For every element"?

Is there a mathematical symbol that means "For every element"? I want the meaning to have similar function as an iteration, say for loop.

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What is the remainder when 1!+2!+3!+4!+5!+.......+50! is divided by 5!?

What is the remainder when 1!+2!+3!+4!+5!+.......+50! is divided by 5! My Approach $1$+$2$+$6$+$24$+$5$!/$5$!+$6 . 5$!/$5$!+$7$ .$6$ . $5$!/$5$!....so on ...

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Derivative of $\sin^n(x)$ by first principle

How can we find the derivative of the function $f$ defined by $$f(x)=\sin^n(x)$$ by first principle of derivative, i.e. by calculating the limit $$f'...

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How to solve for $~ 2x - \tan(x)=0~$

I need to find the roots for this function $$~ 2x - \tan(x)=0~$$ in order to graph it. I have found the one root $~(x=0)~$ but there are two more $~(x= -1...

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How to order functions by their rate of growth? [closed]

I have the following functions. \begin{align} &7n^3 + 3n\\ &4n^2\\ &\frac{12\log(n)}{\log(n)}\\ &\frac{1}{n^2}+18n^5\\ &e^{\log\log n}...

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Equivalent ideas of absolute continuity of measures

Wikipedia says that $\mu$ is absolutely continuous with respect to $\nu$, if $\nu(A)=0 \Rightarrow \mu(A)=0$. Okay, then I found another notion of absolut...

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How many 10-letter words can you make using 3 A's, 4 B's, and the rest could be any letter from a 24-letter alphabet?

How many 10-letter words (they don't have to be actual words) can you make using 3 A's, 4 B's and the rest could be any letter from a 24-le...

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How many integers between $10000$ and $99999$ ( inclusive) are divisible by $3$ or $5$ or $7$?

How many integers between $10000$ and $99999$ (inclusive) are divisible by $3$ or $5$ or $7$ ? My Try : Total Integers between $10000$ and $99999$ are $89...

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Question on the proof of the spectral mapping theorem for polynomials

Theorem 13.9 in these lecture notes is the polynomial spectral mapping theorem: Theorem 13.9 For a polynomial $p$ we have $\sigma(p(T)) = p(\sigma(T))$. M...

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Possible Properties of a Monotone Function [closed]

I'm working on the following question: Which of the following three properties imply $f$ is monotone (it maybe none or more than 1): $f(x + y) = f(x)...

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