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Jan
27
comment Why $\frac{1}{n}\sum_{j=1}^mj^p \asymp\frac{1}{n}m^{p+1}$ as $n\to\infty$?
Should the denominator on the right side be $p+1$ rather than $n$?
Jan
24
comment Proof of The Associative Law and The Commutative Law.
Is the down-vote because I answered the question as it stood at the time and didn't answer the part about commutativity that was added afterward? Or is there something wrong with my answer?
Jan
22
comment proof that all subgroups of $\mathbb{Z}$ are of the form $H = b\mathbb{Z}$
The last sentence of your question, "But in groups you do the product with other elements of the group, not the same element," is wrong. A group is closed under the operation applied to any two of its elements, whether distinct or equal.
Jan
20
answered deduce the size of the normalizer
Jan
10
comment Group Theory via Category Theory
I think the existence of the Kan extensions, for categories of functors into Set, is always true if the domain categories (in this case G and H) are small. But instead of quoting general results, one can also construct these adjoints explicitly in the case at hand.
Jan
9
comment Group Theory via Category Theory
You could add to item 5 that the functor from [H,Set] to [G,Set] has adjoints on both sides (Kan extensions).
Jan
9
comment Can mathematics get from other sciences what it got from physics?
All we need is another Newton, in a field other than physics.
Jan
9
comment What is $\mbox{Hom}(\mathbb{Z},\mathbb{Z}/n\mathbb{Z})$?
And this answer remains true even if you delete "commutative".
Jan
5
comment Why aren't valid higher order logic sentences recursively enumerable in full semantics?
@AsafKaragila Maybe you're thinking of Cardinal Reinhard Marx (en.wikipedia.org/wiki/Reinhard_Marx)?
Jan
5
awarded  Enlightened
Jan
5
awarded  Nice Answer
Jan
5
comment What is the terminology for “lemma of lemma”
I would use either "sublemma" or "claim"; I think both are fairly common.
Jan
5
answered Is a function changed into another function by a change of variables?
Jan
4
comment how to show that $\int_A f \, d\mu =\mu(A) \int_X f \, d\mu$ when $\mu(E\cap A)=\mu(E) \mu(A)$
If you have the result for characteristic functions, then you can deduce it for linear combinations of those, and then for $L^1$ limits of such linear combinations.
Jan
2
answered Probabilistic Interpretation of Burnside's Lemma
Jan
2
comment Example: $ u\in A \otimes_R B$, but $u \neq a \otimes b $ for any $ a \in A, b \in B.$
What do you mean by "translated"?
Jan
2
comment Continuous function on complete bounded metric space need not be bounded
It's that simple.
Jan
2
comment compatible total order of hasse diagram
AG has given a good way to construct a compatible total order, but in fact this poset is small and simple enough that you can explicitly construct all the compatible total orders. Note that, in any compatible total order, $a$ has to be at the top, and $fdb$ must occur in that order. So all that remains is to figure out where you can insert $e$ and $c$ into the chain $fdba$ (with $e$ below $c$ of course). Unless I've mis-counted, there are just 8 possibilities.
Jan
2
comment compatible total order of hasse diagram
Maybe mention that, in the description of the algorithm, "minimal" means "minimal among the elements not yet chosen". It does not mean, for example, that you need to take all the minimal elements of the original set before proceeding to higher ones. For example, you could do $fdebca$.
Jan
2
comment Holomorphic function is an homeomorphism
The theorem you quoted, about $f$ being an open map, has as a hypothesis that the domain of $f$ is an open set.