8,899 reputation
1646
bio website people.bath.ac.uk/mdp33
location Bath, United Kingdom
age 25
visits member for 2 years, 10 months
seen 13 hours ago

Postgraduate student at the University of Bath, UK, studying geometry and representation theory. Currently thinking about cluster algebras and related objects.


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.
Oct
23
revised Transpose of composition of functions
added 8 characters in body
Oct
22
revised Showing $\mathbb{H}$ is isomorphic to a subring of $M_2(\mathbb{C})$ as $\mathbb{R}$-algebras
added 13 characters in body
Oct
22
comment Linear Algebra Subspace question
Admittedly I don't know what happened to them many years later...but they were certainly able to solve linear algebra problems comfortably by the end of the course. I might be a little concerned if they were consistently making algebra mistakes like $b_1b_2=0\implies b_1=b_2=0$, but there's no evidence here that that was any more than a one-off error.