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seen Oct 16 at 23:08

Studying maths in a higher semester.


Oct
16
comment If $P$ denotes the Cantor set, then show that $[0, 1] \setminus P$ is dense in $[0, 1]$
math.stackexchange.com/help/notation should help you fix this. note that a backslash is \setminus, the character $\setminus$ is reserved.
Oct
16
comment Is This Set a Group? Ring?
Note that $(G, \circ)$ is not even a group because $m=0$, i.e. $f(x)\equiv b$ has no inverse.
Oct
16
comment Is This Set a Group? Ring?
You mean $(G, \cdot)$ is not a group, since $(G, +)$ is a group.
Oct
16
answered Two sets are disjoint if and only if one is contained in the complement of the other
Oct
16
revised Two sets are disjoint if and only if one is contained in the complement of the other
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Oct
16
revised the probability of existence sequence
added 2 characters in body; edited tags
Oct
16
comment the probability of existence sequence
Simple: $p^k (q-k+1)$ that gives a probability for $S = (\ldots, A, A, \ldots, A, \ldots)$ with $k$ (or more) apples in succession.
Oct
16
comment naming n-dimensional triangulation
@JaviV Thanks for the references, you may want to add them to the answer to back it up ;)
Oct
16
comment the probability of existence sequence
Depends on the length of the sequence.
Oct
16
revised linear word problem 2
edited tags
Oct
16
comment naming n-dimensional triangulation
@JaviV I could only find this topology related one and this plus a book "Progress in Pattern Recognition, ...". Seems rarely used. About $400$ results vs. $1,700,000$ for "triangulation"
Oct
16
revised Extremely ($90$%) biased coins. What information can we derive/assume based on results of only $10$ coin flips?
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Oct
16
answered Extremely ($90$%) biased coins. What information can we derive/assume based on results of only $10$ coin flips?
Oct
16
comment Extremely ($90$%) biased coins. What information can we derive/assume based on results of only $10$ coin flips?
Not quite. "should" is always a question of taste. If you want to incorporate the event $10H$ in your calculations, you'll be more or less forced to or just forget that it all happened and assume $A$ and $B$ equally likely. What changes is that $P(A|10H) \approx 0.5$ the slighter the bias is. And thus $E(X|10H) \approx 1 + 8\cdot 0.5 = 5$ as expected.
Oct
16
comment naming n-dimensional triangulation
@GrumpyParsnip Do you have any reference? I'd be interested because I have only seen triangulation in literature and papers alike.
Oct
16
comment naming n-dimensional triangulation
Since it's even used for non-simple shapes (Think of NURBS or T-spline surfaces), I hardly believe in any other term. Plus, "simpliciation" is a whole lot harder to pronounce and write than "triangulation". Also note that n-simplices also consist of triangles as their 2D-faces, so the term is not wrong for $n>1$
Oct
16
comment Uniform convergence of $f_n(x) = 1 + x + … + x^n$
Yes it is correct this way. You should put that edit into a complete answer of the question and mark it as solved to help future readers ;) Alternatively pick the best answer and add a comment to it pointing out the details you found.
Oct
16
answered Uniform convergence of $f_n(x) = 1 + x + … + x^n$
Oct
16
revised Uniform convergence of $f_n(x) = 1 + x + … + x^n$
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Oct
16
comment Uniform convergence of $f_n(x) = 1 + x + … + x^n$
Pointwise convergence ($g_n(x) \to 0$) does not imply uniform convergence ($\|g_n\|_\infty \to 0$) in general. Hint: The $r<1$ condition is there for a reason, $f_n \not\to f$ uniformly on $(0,1)$. Only pointwise convergence is guaranteed there.