Reputation
15,021
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
1 17 54
Newest
 Good Answer
Impact
~148k people reached

May
14
comment Regular measure on Borel sets
What is an "official" source? Epimorphic's answer seems perfectly fine, and it does provide suggestions just as you ask. You don't need any source to do the exercise, just the definition.
May
14
comment 51 Dalmatians grouping
I don't really understand the problem. Are you trying to say that we can always choose some set of the dalmatians whose dots add up to a multiple of $11$?
May
14
comment Can the integers be made into a vector space over any Finite Field?
@MartinBrandenburg: True. And of course I should have said that the exponent of a (nontrivial) vector space is the same as the characteristic of the base field.
May
13
comment $S_4$ is not supersolvable? Why am I wrong?
@Sandor: Note that for finite groups, if you only require $G_i$ to be normal in $G_{i-1}$, then it doesn't matter whether you require $G_i/G_{i+1}$ to be just abelian or cyclic, the latter case merely makes the sequence potentially longer. It follows from the fact that a finite abelian group always has a cyclic quotient (which is a consequence of the fundamental theorem on finitely generated abelian groups).
May
13
answered $S_4$ is not supersolvable? Why am I wrong?
May
12
comment Is finiteness necessary in this exercise?
If it has been asked many times before and you know it, you should vote to close as duplicate.
May
12
answered Is finiteness necessary in this exercise?
May
12
awarded  Good Answer
May
12
comment Can the integers be made into a vector space over any Finite Field?
This is kind of roundabout. Also, this argument makes heavy use of axiom of choice (in the form of the statement that vector spaces are free), while the fact that a vector space has the same characteristic as the base field is immediate from the definition.
May
5
comment What is the stone space $S_n(T)$ for a theory with infinitely many equivalence classes, each class infinite?
@MikeHaskel: Also, I don't think you should put too much work into improving the question for OP, either. I'm not saying this is never a good idea, but not in this case: the question is not particularly interesting, and it does seem like rewarding OP for his laziness.
May
5
comment What is the stone space $S_n(T)$ for a theory with infinitely many equivalence classes, each class infinite?
@MikeHaskel: It is clear ot me, too. But it looks like OP didn't even bother to read what he wrote, not to mention showing his work. I don't think such questions deserve an answer, and certainly not one as careful as the one you have given (imho, a one-sentence hint would maybe be okay, if you are feeling generous) -- no offense to you, but I believe it is just detrimental to the site. If the question is improved by OP to fix this bad impression, I will gladly vote to reopen myself.
May
5
comment What is the stone space $S_n(T)$ for a theory with infinitely many equivalence classes, each class infinite?
What is your question? What do you think? You did not even properly type in what the theory is...
May
4
answered $\langle A,B\rangle = \operatorname{tr}(B^*A)$
Apr
29
comment Differential operator is not continuous between this metric spaces
@TravisJ: yes, that works. You can also just cut off at some point before $0$ and then use some kind of mollifier or another "smoothing" method. That would give you a global, smooth function on ${\bf R}$, but it takes some more work to do that formally. Shifting is easier if you just want a function on $[0,1]$.
Apr
29
awarded  Yearling
Apr
29
comment Differential operator is not continuous between this metric spaces
@TravisJ: I have not said that they are already good enough. I'm not solving your exercise, just hinting. You need to fix them (both to be defined and differentiable in $[0,1]$ and to stay close to $0$).
Apr
29
answered Differential operator is not continuous between this metric spaces
Apr
29
reviewed Leave Open Differential operator is not continuous between this metric spaces
Apr
28
comment Category of $\mathcal{L}$-structures
Yeah, I don't see any point of restricting to relational languages. It just makes half of the examples you cited awkward to use with this. Also this seems way to broad to answer. What kind of properties are you asking about? I don't think you can say anything meaningful in general, besides. I have a hunch that any category is (isomorphic to) a full subcategory of one like this, heck, I think it's reasonable to think that it is true for concrete categories (along with the forgetful functor).
Apr
26
comment “Cascade induction”?
Again, consider $\varphi(n)=(1897| S_n\land 1897| T_n\land 1897|U_n)$. Then you can prove $\varphi(n)$ by standard induction.