2h
answered supremum of a function in a normed space
2h
revised supremum of a function in a normed space
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11h
revised Completeness of $\ell^2$ space
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11h
revised show that $l^2$ is a Hilbert space
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11h
revised If $\sum_{n=1}^{\infty}x_n^2<\infty$ and $\sum_{m=1}^{\infty}x_n^2<\infty$, is $\sum_{k=1}^{\infty}(x_n)_k^2(x_m)_k^2<\infty$?
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11h
comment what is non trivial basis for cofinite topology on non empty set $X$
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11h
reviewed Close what is non trivial basis for cofinite topology on non empty set $X$
11h
revised Deriving the formula for the $n^{th}$ tetrahedral number
added Wikipedia link
12h
revised Given a normal $A_{n\times n}$ matrix, then $\lVert A^*v \rVert = \lVert Av\rVert$ and $\langle Av,v\rangle = \langle A^*v,v\rangle$
TeX: \langle, \rangle
12h
comment Deriving the formula for the $n^{th}$ tetrahedral number
Maybe it is also interesting to mention that this is a special case of Hockey-Stick identity, where the lower index is $2$. math.stackexchange.com/questions/1490794/… artofproblemsolving.com/wiki/index.php/… math.stackexchange.com/questions/linked/833451
12h
comment Simplify triangular sum of triangular numbers: $\sum_{i=1}^{n}(\frac12i(i+1))$
This also can be considered as a special case of Hockey-Stick identity, where the lower index is $2$. math.stackexchange.com/questions/1490794/… artofproblemsolving.com/wiki/index.php/… math.stackexchange.com/questions/linked/833451
12h
revised Evaluate $\sum\limits_{k=1}^n k^2$ and $\sum\limits_{k=1}^n k(k+1)$ combinatorially
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12h
comment Simplify triangular sum of triangular numbers: $\sum_{i=1}^{n}(\frac12i(i+1))$
Isn't this simply tetrahedral number (a.k.a. triangular pyramidal number)? en.wikipedia.org/wiki/Tetrahedral_number math.stackexchange.com/questions/1475083/…
12h
revised Is the symmetric group $S_4$ cyclic
TeX: \langle, \rangle
12h
comment Is the symmetric group $S_4$ cyclic
See also more general question: Are there any Symmetric Groups that are cyclic?
12h
revised Is the symmetric group $S_4$ cyclic
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12h
revised Prove that the symmetric group $S_n$, $n \geq 3$, has trivial center.
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12h
revised Are there any Symmetric Groups that are cyclic?
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12h
revised Prove by mathematical induction: $\frac{1}{n}+\frac{1}{n+1}+\dots+\frac{1}{n^2}>1$
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12h
comment Prove that $\frac 12\leq \frac{1}{n+1}+\frac {1}{n+2}+\frac{1}{n+3}...+\frac{1}{n+n}$
You can find several posts showing that this is at least $\frac{13}{24}$. For example math.stackexchange.com/questions/508664/…
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