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Apr
11
answered If we toss one coin twice, what would be the Sample Space?
Apr
11
comment Some limit questions around $1$
Hint: Sequence 1 is positive and decreasing.
Apr
11
comment Mathematically what are random numbers?
@Ryan: That's actually true for the universe. We have derived formulas that accurately describe what we have observed up to now. We just assume that they also will describe anything we will observe in the future, simply because they worked so well in the past, and we see no reason that they would stop working in the future. But actually we cannot know for sure that the world will not stop to behave that way tomorrow.
Apr
11
comment Mathematically what are random numbers?
In mathematics, sequences are generally infinite.
Apr
11
comment Why is the negation of $A \Rightarrow B$ not $A \Rightarrow \lnot B$?
But "knowing" that France is not in Europe also tells me nothing about the future, and yet "France is not in Europe" does imply "I will win the lottery" because implications from false statements are always true.
Apr
11
answered Why is the negation of $A \Rightarrow B$ not $A \Rightarrow \lnot B$?
Apr
10
answered Why do we think of group compositions as multiplication?
Apr
10
comment Integral for which numeric methods will always give an incorrect result?
If you want to numerically integrate this function, you must first numerically implement it. How would you do that?
Apr
9
answered Uniqueness of probability given marginals
Apr
9
comment Linear algebra, nilpotent matrix, rank
Also a hint at 5: Try diagonal matrices (note 2+2=4)
Apr
9
comment Linear algebra, nilpotent matrix, rank
1: Exactly. 2: Yes, that works.
Apr
9
comment Linear algebra, nilpotent matrix, rank
Hint for 1: The simplest rank-1 matrices have only one non-zero entry. Where do you have to put that entry to make $A^2=0$? Hint for 2: Think block matrix, and use the hint for 1.
Apr
9
comment Find the values of $a$ and $b$ that make $f$ differentiable at $x=0$
Why do you think that $a=0$ and $b=0$?
Apr
9
comment Find the values of $a$ and $b$ that make $f$ differentiable at $x=0$
What did you try?
Apr
9
revised Find the values of $a$ and $b$ that make $f$ differentiable at $x=0$
LaTeX formatting
Apr
9
comment Do commuting matrices share the same eigenvectors?
@RickyDemer: But then, for $n=0$ the claim is trivially true, not trivially false, since in that case the sets of eigenvectors (always the empty set, since eigenvectors are by definition non-zero) of any commuting matrices $A$ and $B$ (where we always have $A=B$) are identical.
Apr
9
comment A number $n$ which is the sum of all numbers $k$ with $\sigma(k)=n$?
Instead of just writing "a well-known multiplicative number-theoretic function" is would be more useful to either shortly say what it is, or if that's not possible, link to an appropriate description (e.g. on Wikipedia or MathWorld).
Apr
9
comment Do commuting matrices share the same eigenvectors?
"but no non-identity matrix has this property." — Wrong. For every number $c$, the matrix $cI$ also has that property. For $c\ne 1$ that matrix clearly is not the identity matrix (for $c=0$ it doesn't even have the same rank).
Apr
9
comment Convex hull of set of sparse vectors?
The convex hull of sufficiently many sparse vectors might contain non-sparse vectors. Where is the problem?
Apr
9
revised A pedagogical proof that 9's can be ignored when calculating digital roots
added 11 characters in body