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1d
comment Diffie-Hellman Constructing a secret-sharing scheme
Alice sends Bob the value "I don't know what to send." Bob sends Alice the value "Nor do I." The shared secret is that both don't know how the algorithm works. ;-)
1d
comment Is it possible that “A counter-example exists but it cannot be found”
I forgot the @TrevorWilson in the previous comment.
2d
comment Average Line of a Set of Lines
I'd say that completely depends on what you need the average line for (that is, what you want the average line to tell you), and/or where the original lines come from (indeed, this may decide whether the concept of an average line is actually meaningful in your context).
2d
reviewed Reject suggested edit on $b_k = \sum\limits_{j=0}^4 j\omega^{-kj}$, for $0\le k\le4$ $\Rightarrow$ $\sum\limits_{k=0}^4 b_k\omega^k$ =?
2d
comment Prove that if $G$ is a group and $H$ is a subgroup of $G$ generated by all elements of order $N$ in $G$, then $H$ is a normal subgroup of $G$.
But $H$ is generated by the elements of order $N$. So for each $h\in H$, $h=h_1h_2h_3\dots$ where each $h_i$ is of order $N$. And $ghg^{-1} = (gh_1g^{-1}) (gh_2g^{-1}) (gh_3g^{-1}) \dots$, with each factor being of order $N$.
2d
comment Prove that if $G$ is a group and $H$ is a subgroup of $G$ generated by all elements of order $N$ in $G$, then $H$ is a normal subgroup of $G$.
You're welcome.
2d
comment Prove that if $G$ is a group and $H$ is a subgroup of $G$ generated by all elements of order $N$ in $G$, then $H$ is a normal subgroup of $G$.
And if $h$ is an element of order $N$, then this is ...
2d
comment How to proof that the velocity field u is always $\nabla\cdot$ u=o except at the origin.
What about simply calculating $\nabla\cdot \mathbf u$?
2d
comment Prove that if $G$ is a group and $H$ is a subgroup of $G$ generated by all elements of order $N$ in $G$, then $H$ is a normal subgroup of $G$.
What is $(ghg^{-1})^N$?
2d
comment Proof that $e^x$ is the eigenvector or the derivative operator
"You can (illustratively and not very well defined) understand a function as an infinitely dense vectors with values at $y(x)$. But then it makes no sense to talk about vectors at all." Of course it does, and it is actually very well defined. It's probably not very useful, and you'll certainly not be able to write down a basis, but it is well defined (indeed, it's exactly the definition of a function!) and a valid vector space. The only problematic term in your description is "infinitely dense" because that requires a topology; I don't know if a reasonable one can be defined in that case.
2d
comment 2.71828. And then another 1828.
Here's another thing to "worry" about. Look at the first 30 digits of the decimal expansion of $\pi$. And search for the pattern "aba". What do you find? $3.\color{red}{\,141\,} 5926 \color{red}{\,535\,} 8 \color{red}{\,979\,323\,} 84 \color{red}{\,626\,} 43 \color{red}{\,383\,} 279$. What are four digits repeated once compared with that? :-)
2d
awarded  Nice Question
2d
comment Reflexive for belonging ($\in$)
@Sibi: Because one could imagine that there are sets which contain themselves as elements, for example $A=\{A\}$. For that set, if it existed, $A\in A$ would be true.
2d
comment Reflexive for belonging ($\in$)
@Sibi: $\in$ is "is element of". The set $\{0,1\}$ has two elements, namely $0$ and $1$. That is, $x\in A$ if and only if either $x=0$ or $x=1$.
2d
comment Reflexive for belonging ($\in$)
Actually, in the standard construction, $0$ and $1$ are sets, namely the empty set, and the set containing (only) the empty set. Indeed in that construction, $A$ is also a number, namely the number $2$.
2d
comment How many different messages can be transmitted in n microseconds using three different signals…
You can also start at $0$ by noting there's exactly one message you can send in $0$ microseconds, namely the empty message (no signal). Then the recursion naturally gives you $a_2=a_1+2a_0=1+2\cdot 1=3$.
2d
comment Knot theory: Braids
Did you try drawing both braids?
2d
comment If $A + B = \frac{\pi}{3} (A,B>0),$ Then the minimum value of sec A + sec B is?
Hint: $B=\pi/3-A$
2d
revised Plotting a region in $3D$ space
added 74 characters in body
2d
revised Plotting a region in $3D$ space
Added labels and image example