6:27 AM
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I just want some quick clarification on some notation. If we have a variable defined by a function, such as: $$Z=f(E)$$ then we know both of these are different notations for the derivative: $$\frac{dZ}{dE}=f'(E)$$ If instead I see this notation $$\frac{d(Z/E)}{dE}$$ and I let $$g(E)=f(E)/E$$ doe...

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For any positive integer $n$ the left factorial function is defined as $$!n = 0!+1!+2!+\cdots+(n-1)!$$ My work: Consider a $p$-dimensional Euclidean space with orthogonal coordinates, and take the two vectors $$X = [ 0!, 1!, 2!,\cdots, (p-1)! ]$$ $$Y = [ (p-1)!,\cdots, 2!, 1!, 0! ]$$ The dot p...

In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively.Consider y as a function of a variable x, or y = f(x). If this is the case, then the derivative of y with respect to x, which later came to be viewed as the limit lim Δ x → 0...
It seems that the term "left factorial" is commonly used in a different meaning: Derangement
> The number of derangements of a set of size n is known as the subfactorial of n or the n-th derangement number or n-th de Montmort number. Notations for subfactorials in common use include !n, Dn, dn, or n¡
In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. In other words, a derangement is a permutation that has no fixed points. The number of derangements of a set of size n is known as the subfactorial of n or the n-th derangement number or n-th de Montmort number. Notations for subfactorials in common use include !n, Dn, dn, or n¡.For n>0, the subfactorial !n equals the nearest integer to n!/e, where n! denotes the factorial of n and e is Euler's number.The problem of counting derangements was first considered...

3 hours later…
9:10 AM
in Buraian's not so secret hideout, 19 secs ago, by Martin Sleziak
@Beautifullyirrational Concerning your recent post on meta, maybe and might be suitable tags: Why did my question receive a negative reception?
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I had recently asked this question which shortly after posting got three downvotes. I can't seem to understand why. I suspect that it has something to do with the level of how speculative it is. However I think it was somewhat unjust. To be more elaborate, the reason I thought that the question g...