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comment Square roots of Complex Number.
"first equation" $\: \mapsto \:$ "second equation" $\;\;\;$ ? $\;\;\;\;\;\;\;\;$
May
15
comment Is the logarithm of $\aleph_0$ infinite?
@Omnomnomnom : $\:$ I specifically addressed that possibility in my comments to André's answer. $\hspace{.53 in}$
May
11
revised How can one solve an equation over over a specific finite field?
fixed grammar
May
9
awarded  Fanatic
May
8
comment Can a multiply-periodic complex function be analytic?
How do you evaluate that sum? $\:$ (If I'm figuring things right, then there is no point at which it converges absolutely.) $\;\;\;\;$
May
7
comment Is the logarithm of $\aleph_0$ infinite?
It also can't be incomparable with $\aleph_0$, since otherwise one could compose a bijection with the singleton map $\: X\to 2^X \:$ to get an injection into $\omega$.
May
7
comment Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
You start with further clarification of what you mean by "does not apply generally". $\;$
May
6
comment Two cards are drawn from a deck of 52. Let event A be that two cards have the same value and event B be the same suit. Are these independent?
They are also independent if $\: P(B) = 0 \;$. $\;\;\;\;$
May
5
comment Why can't differentiability be generalized as nicely as continuity?
One can replace $\mathbb{R}^n$ with a (T$_0$) topological vector space. $\;$
May
4
answered Traveling salesman “with tunnels”
May
2
comment TI-84 gives 100 for d/dx(cube_root(x)) at x=0
Presumably it's using $\: h = 0.001 \:$ to approximate the derivative. $\;\;\;\;$
May
1
comment Proving a polynomial has a solution in the interval (0,1)
point $\mapsto$ root $\;$
May
1
comment Quick solution check for the TSP
(… continued) $\;\;\;$ determine "how accurate a discretization would have to be to guarantee that the discretization preserves optimality" backwards, and when those discretizations are sufficiently accurate, those algorithms can be used to find a positive integer $s$ such that the discretized lengths of non-optimal routes are greater than [the smallest discretized cost plus $s$] and the discretized lengths of optimal routes are less than [the smallest discretized cost plus $s$]. $\;\;\;\;$
May
1
comment Quick solution check for the TSP
DVD's point about my now-deleted comment about discretization is very good; I don't see any reason why the discretization would preserve optimality forwards. $\:$ It's true that one "can discretize the problem by approximating the distances with rational numbers and then clearing denominators" (as I mentioned in that comment). $\:$ The lower bounds described in these two papers can be used to $\;\;\;$ (continued …) $\;\;\;\;\;\;\;$
May
1
comment Quick solution check for the TSP
One can provably solve the problem with only a polynomial amount of memory by implementing $\hspace{.53 in}$ the algorithm that corresponds to the composition of Proposition 1.1 and Theorem 4.1. $\hspace{1.15 in}$
May
1
comment Quick solution check for the TSP
(I fixed the grammatical error in my previous comment.) $\;$
May
1
comment Quick solution check for the TSP
A path can't be "the shortest possible one" if there are other paths of the same length. $\hspace{.9 in}$ (However, in that case, it could still be "a shortest possible one".) $\;\;\;\;$
May
1
comment Quick solution check for the TSP
"How does one convert them for" what "binary code?" $\:$ From the paper I linked to in my previous comment: "the best known result so far ABKPM09 is containment in the counting hierarchy CH, which is a subclass of PSPACE ...". $\;\;\;\;$
May
1
comment Quick solution check for the TSP
If the distances are irrational then the problem is either Euclidean TSP or some other variation of the TSP. $\;$
May
1
answered Quick solution check for the TSP