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Oct
25
comment If the variance is $0$ is it constant?
"almost surely constant" $\: \neq \:$ "constant" $\;$, $\;$ although in most cases the difference does not matter. $\hspace{.64 in}$
Oct
25
comment If the variance is $0$ is it constant?
If "the variance of some random variable is 0" then it is almost surely constant. $\;$
Oct
22
comment Proving that every connected graph has a vertex whose removal will not disconnect the graph.
Either graphs with exactly one vertex are counterexamples or the empty graph is a counterexample, depending on whether or not the empty graph counts as connected. $\;$
Oct
20
comment Linear approximation of $ e^x near x-0 $
@aero26 : $\:$ Do you mean "$\hspace{-0.02 in}e^x$ near $x\hspace{-0.04 in}=\hspace{-0.04 in}0$"? $\;\;\;\;$
Oct
19
asked Can an orderable field always be ordered in a way that extends a given subfield's ordering?
Oct
19
comment A function having limit at every point but continuous nowhere
Since those sets are discrete subsets of a second-countable space, they can be given canonical enumerations. $\:$ (Take a countable basis, and enumerate each set according to the first basic subset whose intersection with the discrete set in exactly the given element.) $\:$ Thus the Axiom of Choice is not needed for the OP. $\;\;\;\;$
Oct
18
comment Is abstract algebra (mostly?) restricted to $2$-ary operators?
It's not something one would "stumble upon", but Wikipedia has an article about median algebras. $\hspace{.51 in}$
Oct
13
comment How do I find this partial derivative
Is the "$u(x,y) = \ldots \:$ and $u(0,0) = 0$" line a quote from the assignment? $\;\;\;$
Oct
11
comment Find the limit as $x$ approaches $5$
@Kabama : $\:$ It's like canceling the 3s to go from $\frac{13}{23}$ to $\frac12$. $\;\;\;\;$
Oct
6
comment How are the Stirling-based bounds for the factorial function proven?
I just did that. $\:$ I see the wikipedia article, the article I linked to, a proof of the approximation, something that could be combined with Stirling's formula to prove a non-strict version of the upper bound I'm asking about, a physics reference that does nothing like proving it, another proof of the approximation, two citations to the link I gave in my OP, a page that states very weak bounds and proves the approximation, and two more proofs of the approximation. $\:$ In summary, although there are lots of "proofs of Stirling's formula around", those don't help me. $\;\;\;\;$
Oct
6
asked How are the Stirling-based bounds for the factorial function proven?
Oct
4
answered Is it possible to show that the addition of two Cauchy sequences in $\mathbb R^n$ is also Cauchy for any metric?
Oct
3
revised How can one handle very large numbers such as ${1,000,000 \choose 500,000}$ using binomial formula and very tiny numbers such as $0.5^{1,000,000}$?
fixed title's grammar
Oct
3
comment Does continuous distribution function mean continuous random variable
en.wikipedia.org/wiki/Cantor_function $\;$
Sep
30
comment Prove that there are infinitely many integer solutions to a diophantine equation
"infinite integer" $\: \mapsto \:$ "infinitely many integer" $\;\;\;$ ? $\;\;\;\;\;\;\;$
Sep
29
comment Does the implicit function theorem hold for discontinuously differentiable functions?
I have cross-posted this to mathoverflow. $\;$
Sep
28
comment I can't understand logical implication
$A\implies B \;\;\;\;$ means $\;\;\; \operatorname{truthvalue}(A) \leq \operatorname{truthvalue}(B) \;\;\;$. $\;\;\;\;\;\;\;$
Sep
27
comment How to determine if 3 points on a 3-D graph are collinear?
Counterexample: $(0,0,0),(0,0,0)$ and $(1,1,1) \;$
Sep
26
revised How can the completeness of Hilbert's axioms be proven?
fixed grammar
Sep
25
comment If ${T_n}$ is a sequence of sets that converges to the set of irrational numbers, does $\overline{T_n}$ contain an interval for some $n$?
So, the sequence $\:\mathbb{R},\hspace{-0.03 in}\mathbb{R},\hspace{-0.03 in}\mathbb{R},...\:$ converges to the set of irrational numbers? $\;\;\;\;$