222 reputation
112
bio website facebook.com/…
location Newcastle, Australia
age 28
visits member for 2 years, 4 months
seen May 3 '13 at 5:37

Undergraduate mathematics student interested in functional analysis.


May
3
comment Characterisation of the spectrum of certain unitary representations on $L^2(G)$
If it helps, I am mostly concerned with translation operators such as the left and right regular representations.
May
3
revised Characterisation of the spectrum of certain unitary representations on $L^2(G)$
edited title
May
3
asked Characterisation of the spectrum of certain unitary representations on $L^2(G)$
Dec
5
awarded  Yearling
Feb
20
comment Proof that $n^3+2n$ is divisible by 3
Try expanding $(n+1)^3 + 2(n+1)$ and note that you have assumed $n^3 +2n$ is assumed divisible by 3. What does this tell you about the $n+1$th case?
Jan
31
revised prove for all $n\geq 0$ that $3 \mid n^3+6n^2+11n+6$
Latex Edit
Jan
31
suggested suggested edit on prove for all $n\geq 0$ that $3 \mid n^3+6n^2+11n+6$
Jan
31
comment prove for all $n\geq 0$ that $3 \mid n^3+6n^2+11n+6$
Induction will be handy here.
Jan
30
comment An open ball is an open set
Shouldn't the last part of the inequality be $d(x,y)+d(y,x_0) < r_1+ d(y,x_0) = r$?
Jan
25
revised Cauchy's convergence criterion
added 32 characters in body
Jan
25
answered Cauchy's convergence criterion
Jan
24
comment Alternate definition of closed set in $\mathbb{R}$
@JonasMeyer: It's a bit of an abuse of the function notation (or maybe just wrong). I was trying to say that some sort of structure should be shown with $\mathbb{R}$ in the space where the dot was placed just so the community knows whether the OP is dealing in a metric space or a strictly topological space. Sorry for the confusion/bad notation.
Jan
24
comment Alternate definition of closed set in $\mathbb{R}$
Yes, the standard topology on $\mathbb{R}$ is what would be assumed. I was more implying that it should have been stated that it was a metric space. The balls make that obvious here though.
Jan
24
comment Alternate definition of closed set in $\mathbb{R}$
It helps if you specify the topological structure of $(\mathbb{R},\cdot)$ in the question.
Jan
23
comment Convergence of Infinite Series
You'll have a hard time with that one. If you factor out the half, then you are left with the harmonic series.
Jan
23
comment Closure of $A \subset \mathbb{R}$
Ah yes, sorry about that. To ammend the proof strategy that I have provided, you must assume that an element of $bdry(A)$ is either a limit point or an isolated point of both $A$ and $X\backslash A$ and then argue for both cases that it cannot be an interior point.
Jan
23
comment Closure of $A \subset \mathbb{R}$
$bdry(A)$ is the set of limit points of $A$ that are also limit points of $X\backslash A$. Then you need to show that a boundry point is an element of $\bar{A}$ that cannot be an interior point. Hence from $bdry(A) = \bar{A}\backslash int{A}$, the result follows.
Jan
20
comment Linear operator's linearity
The $z^2$ vanishes with the choice of $a$.
Jan
20
comment Linear operator's linearity
Yes, don't mind me. I confused myself for a second.
Jan
20
comment Linear operator's linearity
Once you have found your $n$ and $a$, you can write the matrix representation of $f \,$ by considering $f$'s actions on the standard basis for $\mathbb{R}^n$.