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1h
comment Doubt on the comparison test: can I still evaluate $\lim \limits_{n \to \infty} \frac{a_{n}}{b_{n}}$ if $b_{n}$ might be $0$ for some $n$?
If i happens that $b_n = 0 $ implies $a_n = 0$, you can.
12h
comment Similarity of a specific block matrix
For some reason, I always find the Kronecker product a little intimidating. Perhaps a throw back from the days of 8kb computers :-).
23h
comment Similarity of a specific block matrix
Presumably you meant $A$ ($n-1$) times?
1d
comment Probability of being between two independent Gaussian random variables
If $\phi(x) = P(X \le x \le Y)$ then $\phi(x) \to 0$ as $|x| \to \infty$. if $X,Y$ have continuous distributions (they do) then $\phi$ has a maximum (regardless of independence).
1d
comment Inverse of $I +T^*T$
What context, a Hilbert space?
1d
comment does constant convexity assures global minimum
I added some detail above.
1d
revised does constant convexity assures global minimum
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1d
revised a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$
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1d
revised a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$
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1d
comment a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$
@Hans: Are you familiar with the notion that $S$ is closed iff for all sequences $x_n \to x$ with $x_n \in S$, then $x \in S$? I added an alternative proof of closure.
1d
comment Confused about proof that diameter of a closure of a set is the same as the diameter of the set.
Fix $\epsilon$. Then for any $p,q$ you can find $p',q'$ so that the relationship holds. The right hand side only depends on $\epsilon$.
1d
comment Confused about proof that diameter of a closure of a set is the same as the diameter of the set.
I see what you are asking. If you have $x \le L$ for all $x \in S$, then you have $\sup S \le L$. Here we have $d(p,q) \le ...$, where the right hand side is a fixed quantity, hence it is true for the $\sup.$
1d
comment Confused about proof that diameter of a closure of a set is the same as the diameter of the set.
Since $p',q' \in E$ then $d(p',q') \le \operatorname{diam} E$.
1d
answered a set $S \subseteq \mathbb{R}$ is closed and bounded if and only if every sequence in $S$ has a sub sequence converging to a point of $S$
1d
revised solution to differential equation from deriving power series
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1d
revised solution to differential equation from deriving power series
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1d
answered solution to differential equation from deriving power series
1d
comment Laplace transforms to solve heat equation
@T.A.E.: It is also entirely feasible, as is often the case, that I missed a point :-).
1d
comment Laplace transforms to solve heat equation
@T.A.E.: Thanks. I realise that for nice $u$ that $L(u_{xx}) = (L(u))_{xx}$, but perhaps this is where the OP was stumbling?
1d
comment Laplace transforms to solve heat equation
@AntonioVargas: Did you mean $L((u)_{xx})$?