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May
28
comment Why do we need $\sup$ and $\inf$ when we have $\max$ and $\min$.
Consider the maximum value for a function for which the range is $[0,b)$.
Mar
9
awarded  Popular Question
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 approved 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
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 $\sum_{n=1}^\infty\frac{1}{2\cdot n}$
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.