John Bentin
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Registered User
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2d |
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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. |
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May 5 |
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Modern Mathematical Achievements Accessible to Undergraduates Do you mean the symmetric matrix associated with the quadratic form? |
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Apr 30 |
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Number of Distinct Sums of Integers You talk about "subsets" of $S$, but then you have discarded the multiset structure of $S$. Do you mean sub-multisets of $S$? |
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Apr 2 |
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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 $x$? |
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Apr 1 |
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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". |
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Apr 1 |
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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, $a=1/\mathrm e$. |
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Apr 1 |
asked | Which compositions have these sum-like and product-like properties on the positive reals? |
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Mar 26 |
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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 $c$"? |
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Mar 24 |
asked | Which real scalings of the natural numbers approximately accommodate the unbounded powers of a noninteger? |
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Jan 7 |
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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) $x$? |
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Jan 1 |
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Approximating erf by tanh Thanks, Aryeh. I was confusing erf with a cumulative distribution function. |
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Jan 1 |
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Approximating erf by tanh Yes. But the function $f$ here doesn't tend to zero at both ends of the interval $[0, \infty)$, because $f(0)=\mathrm{erf}\, 0-\mathrm{tanh}\,0=\frac{1}{2}-0=\frac{1}{2}$. |
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Dec 31 |
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Approximating erf by tanh Sorry, 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. |
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Nov 24 |
answered | I know that you know… |
