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3h
comment Plane intersecting all the lines
@Travis : $\:$ One just needs the Baire category theorem, not measure theory. $\;\;\;\;$
19h
comment Always transcendental? $a + b e^{-x} - f(x) = 0$
... or, for that matter, any piecewise constant function. $\;$
20h
comment I can use MVT on $\lim _{_{x\rightarrow \infty }}\int _0^x\:e^{t^2}dt$?
... and it so happens that the limits of $x$ times them are also equal. $\:$ However, I don't see any reason to believe that happens in the other case. $\;\;\;\;$
20h
comment Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
Trying numbers, I immediately get that $\: n=0 \:$ and $\: n=1 \:$ are counterexamples to your claim that the probability the OP is asking about "turns out to be always 2/3." $\;\;\;\;$
20h
comment I can use MVT on $\lim _{_{x\rightarrow \infty }}\int _0^x\:e^{t^2}dt$?
Their limits are equal; they are usually not equal. $\;\;\;\;$ Consider $\: x\cdot \frac1x \:$ and $\: x\cdot \frac1{2\cdot x} \;$. $\;\;\;\;\;\;\;\;$
21h
comment I can use MVT on $\lim _{_{x\rightarrow \infty }}\int _0^x\:e^{t^2}dt$?
Oh, I was also missing something else. $\:$ You used $\hspace{.04 in}f(x)$ instead of $\hspace{.04 in}f(c)$ near the beginning of your post. $\;\;\;\;$
21h
comment Implications of Inner product vs Norm vs Metric Space
Your inner product lines still have the problem that Travis pointed out. $\;$
21h
comment I can use MVT on $\lim _{_{x\rightarrow \infty }}\int _0^x\:e^{t^2}dt$?
What do you get for $c$ when you "apply the same procedure"? $\;$
1d
comment Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others
Should "one" be replaced with "at least one" or "exactly one" or "a particular"? $\;$
1d
comment Hilbert Space is not locally compact.
"contradiction. Suppose" $\: \mapsto \:$ "contradiction, suppose" $\;\;\;\;$
1d
revised Proof that polynom $P:\mathbb{R}^n\to\mathbb{R}$ is continuous
removed proof-theory tag
1d
revised What should I learn to increase my skill to find proof?
removed proof-theory tag
Apr
15
comment Is the Banach-Tarski paradox realistic? Why is Volume not an invariant?
@MarcvanLeeuwen : $\:$ Yes. $\;\;\;\;$
Apr
13
comment What is the next perfect square of the form 14444… in decimal notation?
"it is sufficient to consider" $\: 0\leq x\leq 5000 \:$, $\:$ since $\: x\mapsto x^2 \:$ is an even function. $\hspace{1.5 in}$
Apr
10
comment If Riemann integrable, then it has finite number of discontinuities
"discontinuous a" $\: \mapsto \:$ "discontinuous on a" $\;\;\;\;$
Apr
9
comment Do commuting matrices share the same eigenvectors?
@celtschk : $\;\;\;$ For $\: n = 0 \:$ those matrices clearly are the identity matrix. $\;\;\;\;\;\;\;$
Apr
7
comment Can Three Equilateral Triangles with Sidelength $s$ Cover A Unit Square?
Erich's Packing Center gives the same configuration as Ross Millikan described. $\;$
Apr
5
comment the limit of $\ln x$ as $x$ approaches $0-$
No. ${}{}{}{}\;$
Apr
5
answered the limit of $\ln x$ as $x$ approaches $0-$
Apr
4
comment Diagonalizing a power set
$f(x)$ would not necessarily have a domain. $\:$ (Also, "constructing a set $T$ not present $\hspace{1.31 in}$ in the domain of" $\hspace{.02 in}f$ is not relevant here. $\;\;\;\;$