1,084 reputation
211
bio website
location Copenhagen, Denmark
age 40
visits member for 1 year, 4 months
seen 10 hours ago

Jul
24
comment If $\phi(n)$ divides $n-1$, prove that $n$ is a product of distinct prime numbers
By the way, no examples are known where $n$ is not actually a prime number, see Lehmer's totient problem.
Jul
20
comment Problem regarding Euler's Theorem: $a^{\phi(n)}\equiv 1 \bmod n$
But $p^2$ is not relatively prime to $n$ ($p$ is a prime dividing $n$) and $p^2$ cannot have a multiplicative inverse!
Jul
15
comment prove that there is maximum and minimum for C[0,1]
What are your difficulties? What have you tried?
Jul
15
comment Solving base e equation
And http://www.wolframalpha.com/input/?i=2Sinh gives a plot (as a function of a real variable), and other info, on $2 \sinh$.
Jul
14
comment Does taking the power set give you the “next biggest cardinal”
See The generalized continuum hypothesis.
Jul
14
comment What exactly is a number?
When in ancient times it was realized that incommensurable quantities exist (like $1:\sqrt{2}$), they did not consider these quantities to be "numbers" (greek (singular) arithmos). Instead, they began "calculating" with geometric objects such as line segments (since this was more general than "numbers" (i.e. $\mathbb{Q}$)). Only later was the concept of number/arithmos generalized to include irrational quantities.
Jul
14
comment When differentiability of the product implies differentiability of the individual terms?
This $h$ is not $C^\infty$ (let alone real analytical) in $x=0$, of course. Maybe no counter-example exists if it is required that $h$ is analytical?
Jul
12
comment Finding if a function is onto?
When you define your $a$, do you check if it is in $\{ x \le 1 \}$? Note that $x \mapsto 2-x$ is onto when viewed as a map $\mathbb{R}\to\mathbb{R}$, but it is not onto as a map $\left( -\infty,1 \right] \to \mathbb{R}$.
Jul
10
comment A problem with the density of sin (N)
@Adimathematica No, the union of two non-dense sets my be dense so there is something missing in my hint.
Jul
10
comment A problem with the density of sin (N)
Since $\sin(-x)=-\sin x$, you would use the fact that $\sin(\mathbb{Z})$ is the union of $\sin(+\mathbb{N})$, $\sin(-\mathbb{N})$ and $\{ \sin(0) \}$. The first two sets are each other's reflections, so if one is not dense, neither is the other.
Jul
7
comment Lamport claims there is an error in Kelley's proof of the Schroeder-Bernstein theorem. What is it?
Yeah, so if we start with a $y_0$ in one of the sets, that point may or may not have a direct ancestor (wrt. the relevant inverse image). If it has a direct ancestor, call it $y_1$ (since it is unique by the injectivty of the relevant map). Then $y_1$ may or may not have a direct ancestor $y_2$. The sequence so produced can be an infinite sequence (direct ancestor can be found forever) or the process can stop after a finite number of steps. But the case where $y_0,y_1,y_2,\ldots$ is well-defined as an infinite sequence, cannot be described as the case where $\{ y_i\}$ is infinite as a set.
Jun
22
comment Limit of a matrix multiplication
That matrix is diagonalizable (with distinct (real) eigenvalues). However, one eigenvalue is exactly $1.0$. So this is very "sensitive" to rounding errors. So don't calculate the matrix powers with binaray floating point computer arithmetic.
Jun
15
awarded  Pundit
Jun
15
comment Conjecture: If $ N $ and $ N + 10 $ are prime, then $ N + 20 $ is composite.
But 3, 13 and 23 are primes (even if one of them is clearly divisible by 3).
Jun
12
comment How to bell curve
Not sure what the question is about. If you have a sample of values $x_i$ with mean $\bar{x}$, you can apply an affine transformation $y=ax+b$ to obtain a mean $\bar{y}=60$ and a maximal value $y_\text{max} <100$.
Jun
12
comment How can one show that ${\rm Hom}\Bigl(\prod\limits_{i\geqslant 1} \Bbb Z,\Bbb Z\Bigr)$ has cardinality less than $2^{\mathfrak c}$?
Wikipedia calls $\prod\limits_{i\geqslant 1} \Bbb Z$ the Baer–Specker group and has references to the original papers too.
Jun
12
comment Can there be a complex line?
Not all reals can be written as $a+b\sqrt{2}$ for $a,b\in\mathbb{Q}$. The set of those which can, is denoted $\mathbb{Q}\left[\sqrt{2}\right]$. It has a different structure than $\mathbb{Q}\left[\sqrt{-1}\right]$. The full set of complex numbers is bigger, $\mathbb{R}\left[\sqrt{-1}\right]$.
Jun
8
comment How to explain the perpendicularity of two lines to a High School student?
@CoolHandLouis In Euclidean geometry the tangent space in one point is naturally identified with the tangent space of another point. So it makes sense to define perpendicularity of lines that do not meet (skew lines). I am not sure if this is done in high schools. For example are the lines $\{(x,y,z)\mid x=0 \wedge y=0\}$ and $\{(x,y,z)\mid x=1 \wedge z=0\}$ perpendicular?
Jun
8
comment How to explain the perpendicularity of two lines to a High School student?
"Lines" without further qualification do not carry an orientation, so rotating a line 90 degrees counterclockwise is the same as rotating it 90 degrees clockwise. I can understand that you regard the line as a kind of trajectory with a "direction", and that is instructive, but from high school definitions a line is just a specific set of points.
Jun
8
comment A generalization of perfect numbers
With ordinary sets, members cannot have "multiplicity", so $\{ 28,28,28,\ldots \} = \{ 28 \}$ with them. Multisets or tuples (ordered) can have the same "entry" duplicated.