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1h
comment If $\mathcal{B}$ is a base of a topology space $\left(X,\tau\right)$, then the Borel $\sigma$-algebra is generated by $\mathcal{B}$?
That's not a complete question, "The Borel $\sigma$-algebra is generated by $\mathcal{B}$?"
3h
comment the golden ratio and a certain simple continued fraction
What does it mean for $k$ to increase with bound if $k$ is restricted to natural numbers? Don't you simply set $k$ to its maximum bound?
9h
comment Specific Root of Interpolating Polynomial
The text box at bottom of screen has "send" button next to it.
9h
comment Specific Root of Interpolating Polynomial
The chatroom is ready for discussion. There are roundabout ways (user scripts) to support MathJax/LaTeX, but chat does not natively do so. However I think I'll be able to interpret "raw" MathJax strings.
19h
comment Can 720! be written as the difference of two positive integer powers of 3?
There aren't many possibilities. Clearly $x \gt y$ and $y$ is the number of factors of 3 in $720!$, which we count to be $y = 356$.
19h
revised Can 720! be written as the difference of two positive integer powers of 3?
clarified title
1d
comment How does the Soundness Theorem follow from this lemma?
Are you clear about the definitions of the two "turnstile" symbols and the meaning of the claim in your "soundness theorem"?
1d
comment Specific Root of Interpolating Polynomial
It is possible. Does an example suffice to satisfy your inquisitiveness?
1d
revised What's the difference between predicate and propositional logic?
responded to comment
1d
comment Finite ring having $2^n-1$ invertible elements
@user265311: The order of the additive group of $A$ is $|A|$. If $|A|$ had an odd prime factor $p$, then by the structure theorem for finite abelian groups, there would be some element $u \neq -u$.
1d
comment Finite ring having $2^n-1$ invertible elements
@DanielFischer: There is a slight gap between this Question and the duplicate cited, namely here the number of non-invertible elements is at most $2^n - 1$ and there the number of non-invertible elements is strictly less than $2^n - 1$. However this only affects the second step of azimut's Answer there, bracketing $2^n - 1 \lt |A| \le 2(2^n - 1)$ where $|A|$ is the size of ring $A$. The conclusion $|A| = 2^n$ remains.
1d
reviewed Leave Closed The motivation for considering exponential families of distributions
1d
reviewed Leave Closed Suppose $f $ is absolutely continuous and that both $f$ and $f'$ are in $L^1 (\Bbb R)$. Prove that $\int_{-\infty}^{\infty} f' (x)dx=0$.
1d
comment Is there a notation for “Bounded Kleene star”?
Would it be possible to expand on this suggested notation a little, at least to the extent of telling Readers whether you've seen this in practice or are just inventing a notation ?
1d
comment How many of each ticket were sold in one day?
It may help Readers if you include the definitions of the variables in your "setup". While it is tempting to interpret $A$ as the number of Adult tickets, $C$ as the number of Child tickets, and $S$ as the number of Senior tickets, the conflation of day one and day two information needs to be explained.
1d
comment How many prime numbers we need?
Perhaps if you would answer with more detail than a one-liner permits, the ambiguity in the question could be pointed out (and ambiguity in your answer removed).
2d
comment Sharing items to a particular number of people
Yes, there would be many ways to do this. It's not constrained mathematically enough to suggest one way is "best", but if you are distributing the prizes, it can be done by an arithmetic series as Theophile suggests, or in some other fashion where the prize differences are small in relation to the total.
2d
comment Is the inclusion map always a module homomorphism?
Yes, the inclusion of a $R[G]$-submodule in a $R[G]$-module is a homomorphism. Here of course the factor $M$ is a "submodule" by way of being a direct factor as a matter of convention, but mapping $m\in M$ to $(m,0)$ is clearly an injective homomorphism.
2d
comment Sharing items to a particular number of people
It seems you have an opinion about how to do this, but it has not been expressed clearly enough in the body of the Question for a solution to be deduced mathematically.
2d
comment Is there a way to visualize a group?
Finite groups are sometimes expressed by their multiplication tables. This does not make it obvious that the associative property holds, but the existence of an identity element and of inverses may be visually checked.