What is the practical application of factorials
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What is the practical application of factorials

I'm trying to understand the practical application of factorial - in simple applications. I searched the math.stackexchange and could not find an ans...

Published: Aug 18, 2026

Natural deduction proof - problem with existential elimination
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Natural deduction proof - problem with existential elimination

I have problems with the following proof: $$ \forall x \exists y (Rxy \land Py), \forall x \neg Rxx \vdash \neg \forall x \forall y (Px \implies (Py \impl...

Published: Aug 18, 2026

25% chance of happening but has to happen 4 times in a row, what is the real chance of happening?
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25% chance of happening but has to happen 4 times in a row, what is the real chance of happening?

Say you need to win 4 times in a row at a 25% success chance for each event, how do I calculate the chance of winning? Overall, how does this calculation ...

Published: Aug 18, 2026

Difference between State Space and Sample Space
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Difference between State Space and Sample Space

Aren't they both the same? According to me they are just different terminologies used for different types of systems. What I understand is that sampl...

Published: Aug 18, 2026

Which value goes on which axis in
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Which value goes on which axis in "plot $a$ against $b$"?

When the question asks to plot $a$ against $b$, which value should go on which axis?

Published: Aug 18, 2026

Can't understand a recursive definition of concatenation of two strings
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Can't understand a recursive definition of concatenation of two strings

I'm reading Rosen's Discrete Mathematics and its applications(6ed), but I can't understand a recursive definition about concatenation of tw...

Published: Aug 18, 2026

Probability of getting a triple when rolling 12 fair 12-sided dice once...
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Probability of getting a triple when rolling 12 fair 12-sided dice once...

There are $12^{12}$ = 8,916,100,448,256 total possible outcomes. I decided to approach it by calculating the probability of rolling the $12$ dice WITHOUT ...

Published: Aug 18, 2026

What is $x \times \sqrt x$
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What is $x \times \sqrt x$

Does $x \times \sqrt x = x$? I thought it was correct because sqrt is the opposite of multiplying by a number, so I figured by multiplying by a number it ...

Published: Aug 18, 2026

Representing $\ln(x)$ as a power series centered at $2$ without computing any derivatives
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Representing $\ln(x)$ as a power series centered at $2$ without computing any derivatives

I am working through a calc book and one of the problems asks the above question. However, taylor and maclaurin series have not been introduced yet. In so...

Published: Aug 18, 2026

What is the number of numbers?
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What is the number of numbers?

For a positive integer $n≥2$, let $f(n)$ denote the smallest prime divisor of $n$. Find the number of integers $n$, $2≤n≤1000$, such that $f(n)=5$. All th...

Published: Aug 18, 2026

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