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| bio | website | |
|---|---|---|
| location | Seattle, WA | |
| age | 42 | |
| visits | member for | 2 years, 9 months |
| seen | 4 mins ago | |
| stats | profile views | 1,366 |
Software engineer and long-time dabbler in mathematics; 11th in the Putnams forever ago but I've long since atrophied.
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16h |
revised |
How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards? Typo correction (it's 'Terence', as the pointed-to link notes, and not 'Tarance') and removal of a few honorifics |
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21h |
comment |
Solve $\sqrt{x+4}-\sqrt{x+1}=1$ for $x$ Note that lab's trick 'always' applies, in some sense; with an equation of form $\sqrt{x+a}-\sqrt{x}=b$ (obviously the given equation can be put into such a form by using $y=x+1$), then by factoring the left side of $x+a-x=a$ one gets $\sqrt{x+a}+\sqrt{x} = \frac{a}{b}$, and then adding/subtracting gives the answer. |
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22h |
comment |
Proving that every term of the sequence is an integer @mathlove I think you're missing my point - I'm suggesting that you build a table of the values $a_{m,n}$ for, say, all $m,n\lt 10$ and see what you see there. |
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1d |
comment |
Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable? As Asaf says, a naive diagonalizability argument won't work here - for instance, it could be the case that $S_i(i)=10$ for all $i$ in the enumeration you choose, in which case you'll never have an $n$ such that $p(n)=10$. |
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1d |
comment |
Proving that every term of the sequence is an integer Have you evaluated the recurrence for various small values of $m,n$? Can you take an educated guess at what $a_{m,n}$ might be? Once you have a good guess as to the form, you may be able to prove that your guess satisfies the recurrence - and once you do that, you're done; the fact that $a_{r,s}$ is defined strictly in terms of values $a_{t,u}$ with $t+u\lt r+s$ means that the solution for any given set of initial conditions must be unique as long as $a_{m,n}\neq 0$ for all $m,n$ (which is easy to show here). |
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May 21 |
comment |
Drawing dynamic circles based on input value This is an important point - whatever the scaling factor, for visualization it's important to have area (and not radius) proportional to population. |
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May 20 |
comment |
What is the order of convergence of Newtons root finding method? And when does it converge? @JoyeuseSaintValentin A root $x$ of multiplicity $m$ is a root for which $f^{(m-1)}(x)=0$ but $f^{(m)}(x)\neq 0$. The motivating example is polynomials; for instance, $f(x)=x^3-4x^2+5x-2=(x-1)^2(x-2)$ has a root of multiplicity $2$ at $x=1$, since $f(1)=0$ and $f'(1)=0$ but $f''(1)=-2\neq 0$. |
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May 20 |
comment |
Geometric representation of product rule? One tiny little tweak I'd make is to replace the $\Delta u\cdot\frac{\Delta v}{\Delta x}$ at the end of the last line with a $\Delta x\cdot\frac{\Delta u}{\Delta x}\cdot\frac{\Delta v}{\Delta x}$ so it's immediately clear that that quantity goes to zero (as long as $u'$ and $v'$ are bounded, of course), as opposed to needing to argue that $\Delta u\to 0$ which can sometimes throw a wrench in the works. |
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May 17 |
comment |
Matrix $BA\neq$$I_{3}$ I would go with your latter thoughts: suppose you have a non-zero vector $v$ such that $Av=0$. Then compute $BAv$ as $B(Av)$ and $(BA)v$... |
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May 17 |
comment |
Knowing that $n= 3598057$ is a product of two different prime numbers and that 20779 a square root of $1$ mod $n$, find prime factorization of $n$. Tiny hint:you know that $(x-1)(x+1)\equiv 0\pmod p$; when can a product of two factors be equal to $0$ modulo a prime? |
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May 15 |
revised |
Integrate: $\int_0^{\infty} \frac{\sin (ax)}{e^{\pi x} \sinh(\pi x)}dx$ TeXified the hyperbolic functions properly |
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May 14 |
awarded | homework |
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May 14 |
answered | Recursion relation for Euler numbers |
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May 14 |
comment |
Recursion relation for Euler numbers My point is that what $E_{2n}$ is and whether the values are positive or alternating varies with your definition - both are relatively commonplace and neither is specifically right (and more to the point, neither is specifically wrong). |
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May 14 |
comment |
Recursion relation for Euler numbers Both definitions are commonly used - because the Euler numbers have combinatorial interpretations it's not unusual to see the $1/\cos(z)$ version, which leads to $E_{2n}$ being positive. See mathworld.wolfram.com/EulerNumber.html |
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May 12 |
comment |
improper integral question - $\int_{1}^{\infty}\!e^{-x}\ln x\,dx$ @user76508 And how did that fail for you? |
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May 12 |
comment |
The Integral that Stumped Feynman? because the tangent function is periodic of period $\pi$, to know what the value is you need to know $10^{100}\bmod\pi$; this is effectively the same as knowing $\pi$ to a hundred places. |
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May 10 |
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$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? I think this question is rescuable as an independent question; the other question specifically asks for geometric ways of constructing $e$, whereas this question asks for intuitive ways of describing $e$ to a layperson, which certainly don't need to be geometric. |
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May 10 |
comment |
Math Behind the Game “Quoridor” What sort of mathematical result are you expecting? At first glance from the rules of the game, it doesn't seem to have any connections to anything particularly deep; the game is just a little bit too dynamic to say anything useful about mathematically. Contrast this against, e.g., Conway's Angels and Devils game, or Piet Hein's Hex, both of which are similar to Quoridor in some senses but with simplicities that make them at some level more 'inherently mathematical'. |
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May 10 |
revised |
$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? Fleshed out slightly, added a different example |
