Reputation
9,149
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
19 49
Newest
 Good Answer
Impact
~158k people reached

Oct
24
comment Group objects in category of $\mathcal{Set}$ are groups - How to prove it?
Here "defines a group" means that the set $G(Z)$ is a group under the binary operation $g\times g'=\mu\circ(g,g')$. (The notation is a bit confusing here; the first $(g,g')$ is a pair of morphisms that you're multiplying to define the group structure on $G(Z)$, whereas the $(g,g')$ in $\mu\circ(g,g')$ is the pair considered as a single map $Z\to G\times G$, by $z\mapsto(g(z),g'(z))$).
Oct
24
revised Quick question: Chern classes of Sym, Wedge, Hom, and Tensor
added 33 characters in body
Oct
24
comment Nature of the range of $e^x$
@pbs Thanks, that's clearer.
Oct
24
comment Nature of the range of $e^x$
All transcendental numbers are irrational, so I'm not sure what the role of the "or" is here. Did you mean to ask if $e^x$ is transcendental whenever $x\ne\log{a}$ for some $a\in\mathbb{Q}$?
Oct
24
comment Finding the co-ordinate vector
You seem to have swapped the roles of $x_1,x_2,x_3,x_4$ and $d,c,b,a$ from the question, which is maybe a little confusing!
Oct
24
comment Finding the co-ordinate vector
I think you might have a typo (or a confusion) in the last line as well - the solution is finding $x_1,x_2,x_3,x_4$, not $a,b,c,d$, which are arbitrary real numbers.
Oct
24
answered Finding the co-ordinate vector
Oct
24
comment Finding the co-ordinate vector
I don't think you meant for $v$ to be what you wrote - perhaps $v=a+bt+ct^2+dt^3$?
Oct
24
revised Finding the co-ordinate vector
deleted 18 characters in body
Oct
24
revised How to Prove that these Spaces are not Homotopically Equivalent
added 37 characters in body
Oct
24
comment Show that $G$ is $2$-connected but not necessarily Hamiltonian
Yes - this is fine! A graph is $n$-connected if you can delete any $k<n$ vertices without disconnecting it, so any $n$-connected graph is also $m$-connected for $m\leq n$. The Petersen graph is $3$-connected, hence $2$-connected.
Oct
24
comment Show that $G$ is $2$-connected but not necessarily Hamiltonian
Why do you think the Petersen graph is not $2$-connected?
Oct
24
revised Show that $G$ is $2$-connected but not necessarily Hamiltonian
added 8 characters in body; edited title
Oct
24
comment Are there definition of percent?
I don't think the problem here is whether or not $1\%=1/100$, but rather what "$5+4\%$" means. Does it mean $5$ whole units plus $4\%$ of an unit, so $5.04$ as in 5xum's answer, or $5$ plus $4\%$ of $5$, which is $5.2$? In the second case, it could more accurately be written as $5\times104\%$. In practice, you will probably have to work out from context (or ask somebody) what is meant.
Oct
23
comment Is continuity in topology well-defined?
@MathewGeorge The second identity might also fail; take the same map as in Hayden's example, then $f^{-1}[f[{x}]]=f^{-1}[{y_0}]=X$ for any point $x\in X$.
Oct
23
answered Applications of Baire's Threom
Oct
23
revised Transpose of composition of functions
added 91 characters in body
Oct
23
comment Transpose of composition of functions
Yes - as long as you can prove equality at some level, it's fine. I was conservative in the suggestion and went all the way down to evaluation on $U$, but as you point out, just playing with composition rules lets you prove equality after evaluation on $W^*$.
Oct
23
answered Transpose of composition of functions
Oct
23
comment Transpose of composition of functions
This is a good idea, because you'll be proving a more fundamental statement. Just write out the definitions of the maps applied to an arbitrary functional and see that they agree! This is fiddly to write down, but ultimately nothing very complicated is happening. If you have already done this but got stuck somewhere, it might help to say what you did.