# John Bentin

 770 Reputation 456 views

## Registered User

 Name John Bentin Member for 2 years Seen 10 hours ago Website Location Age
 2d comment How to determine the number of a cube within a bigger cube? Your latter cube is indeed a cube, but the first-mentioned "cube" is not. Such a rectangular body is called a cuboid. May5 comment Modern Mathematical Achievements Accessible to UndergraduatesDo you mean the symmetric matrix associated with the quadratic form? Apr30 comment Number of Distinct Sums of IntegersYou talk about "subsets" of $S$, but then you have discarded the multiset structure of $S$. Do you mean sub-multisets of $S$? Apr2 comment Which compositions have these sum-like and product-like properties on the positive reals?This is a beautifully clear answer to the question I should have asked. It all seems so simple now! Just one query: In the second line of the proof of lemma 2, should the initial term of the inequalities be $y$, not $x$? Apr1 comment Which compositions have these sum-like and product-like properties on the positive reals?@Todd: Yes, your example works well with, say, $f(x)=x^2$. I would happily take this as the "accepted answer". Apr1 comment Which compositions have these sum-like and product-like properties on the positive reals?@Gerry, @Gerald: I think that Gerry's composition satisfies all the conditions except upper monotony. Take, for example, $a=1/\mathrm e$. Apr1 asked Which compositions have these sum-like and product-like properties on the positive reals? Mar26 comment Which real scalings of the natural numbers approximately accommodate the unbounded powers of a noninteger?Thank you very much for this answer. Just a few queries concerning your 4th paragraph: (1) I can't read "$\sum_1^{\infty}\|\frac{1][\sqrt{5}} \Phi^n\| \lt \infty$"; (2) I guess the equality sign in "$\|x=y\| \le \|x\|+\|y\|$" should be a plus sign; (3) By "$\lambda$ is any real $\lambda=\frac{a}{\sqrt{5}}+b+c\Phi$" do you mean "$\lambda$ is any real of the form $\lambda=\frac{a}{\sqrt{5}}+b+c\Phi$ with integral $a$, $b$, and $c$"? Mar24 asked Which real scalings of the natural numbers approximately accommodate the unbounded powers of a noninteger? Jan7 comment Usage of set theory in undergraduate studies+1, especially for "We should always, always distinguish a function $f$ from its value $f(x)$ at $x$". But I don't get your next point: If we define (say) $y$ := $x^2+1$, then what is wrong with saying that (the variable) $y$ depends on (the variable) $x$? Jan1 comment Approximating erf by tanhThanks, Aryeh. I was confusing erf with a cumulative distribution function. Jan1 comment Approximating erf by tanhYes. But the function $f$ here doesn't tend to zero at both ends of the interval $[0, \infty)$, because $f(0)=\mathrm{erf}\, 0-\mathrm{tanh}\,0=\frac{1}{2}-0=\frac{1}{2}$. Dec31 comment Approximating erf by tanhSorry, I can only see that, on your supposition, $f'$ has $2$ (or more) positive zeros. But anyway that's enough for the rest of the argument to work. Nov24 answered I know that you know…