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Sep
22
awarded  Nice Question
Sep
22
comment Selection through identical balls
Unless you are doing quantum mechanics, "identical" things don't exist.
Sep
22
comment Are there infinitely many “super-palindromes”?
BTW, for the primes of the form $10^k+1$ there's already another math.SE question. Note that according to the discussion linked to by one of the answers, there are no primes for $2<k<16777216$.
Sep
22
comment Are there infinitely many “super-palindromes”?
@MichaelAlbanese: Since all primes of the form $10^k+1$ are palindromic primes, this would imply that there are infinitely many palindromic primes (which as I mentioned is an open question). You are right that it would be sufficient for there to be infinitely many palindromic primes, though.
Sep
22
reviewed Approve suggested edit on Are there infinitely many “super-palindromes”?
Sep
22
comment Statements in Euclidean geometry that appear to be true but aren't
This answer to that question seems directly relevant to me.
Sep
22
asked Are there infinitely many “super-palindromes”?
Sep
22
comment Heat Equation & Fundamental Theorem of Calculus
Note that the whole expression on the left of (1) has two free variables (and none of them is $x$).
Sep
22
comment Can I keep adding more dimensions to complex numbers?
Well, it does break the total ordering property: Unlike for real numbers, there's no total ordering of the complex numbers which is compatible with its algebraic structure.
Sep
22
comment How to divide currency?
The standard monetary series $1,2,5,10,20,50,\dots$ is a compromise between several goals: (1) it should contain the powers of 10, (2) there should be an approximately constant factor between the different values, (3) that approximate constant shouldn't be too large.
Sep
22
comment Show that for vectors $\bf u$ and $\bf v$ in $ℝ^3$, $\bf u \times v = (-v) \times u$
Easier to implement than the trivial component-wise formula (which I guess would even be more efficient because there are no unnecessary multiplications with $1$)?
Sep
22
comment What is $dx$ in integration?
The advantage of writing $\mathrm dx$ at the beginning is that for nested integrals with limits, it's more easily seen which limits belong to which variable, compare $\int_1^2\mathrm dx\int_3^4\mathrm dy\,f(x^2+g(x,y))h(x+y-3)$ with $\int_1^2\int_3^4 f(x^2+g(x,y))h(x+y-3)\,\mathrm dy\,\mathrm dx$
Sep
22
comment Show that for vectors $\bf u$ and $\bf v$ in $ℝ^3$, $\bf u \times v = (-v) \times u$
Which raises the question: Why?
Sep
22
comment Show that for vectors $\bf u$ and $\bf v$ in $ℝ^3$, $\bf u \times v = (-v) \times u$
Note that the question was explicitly about using the properties of the determinant for proving it (otherwise the most obvious proof would be to just calculate both and compare).
Sep
22
comment What is the remainder when $4^{100}$ is divided by 6?
@GeoffRobinson: You surely meant $\frac{2^{199}-2}{3}$.
Sep
22
comment What is the remainder when $4^{100}$ is divided by 6?
But in integer division, $2^{200}/6$ is not the same as $2^{199}/3$. You can easily see this with lower exponentials: $2^4/6 = 16/6 = 2,\text{ remainder }4$ but $2^3/3 = 8/3 = 3,\text{ remainder }2$.
Sep
22
comment Is $[0,1)\times[0,1]$ a linear continuum?
Maybe a way to make the order-isomorphy work would be to use intervals starting at the points of Cantor's discontinuum.
Sep
21
awarded  Custodian
Sep
21
comment Why are measures real-valued?
@NateEldredge: But then, that condition could be put specifically on probability measures instead of measures in general.
Sep
21
comment Is there a bijective map from $(0,1)$ to $\mathbb{R}$?
And the inverse is $f(x)=\ln\left(\frac{1}{x}-1\right)$