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Jul
25
comment Basis, Ordered Basis, and Linear Independence
@SolidSnake, if you write your comments into an answer, then I will accept it. Thank you.
Jul
25
comment The Matrix of $T$ Relative to the Ordered Bases $\mathcal B$ and $\mathcal B'$ for $V$
I know $[T\alpha]_{\mathcal B'}=A[\alpha]_{\mathcal B}\not\Longleftrightarrow[T\alpha]_{\mathcal B}=A[\alpha]_{\mathcal B'}$ because neither $[T\alpha]_{\mathcal C}$ nor $[\alpha]_{\mathcal C}$ might even make sense for some $\mathcal C\in\{\mathcal B,\mathcal B'\}$. What I'm concerned about is whether the bolded definition is ambiguous with my restrictions.
Jul
25
comment Basis, Ordered Basis, and Linear Independence
@SolidSnake, I see. What if it is an ordered basis?
Jul
24
comment Matrix Equation: Reduced Row Echelon Form
Brilliant! I also see the connection between this and Solid Snake's comment regarding elementary matrices.
Jul
24
comment Matrix Equation: Reduced Row Echelon Form
@Tucker, you are correct for that particular case.
Jul
20
comment Hestenes' Existence of Extreme Points
@user251257 You are right. Thank you for your help. If you write your comments into an answer, then I will accept it.
Jul
20
comment Hestenes' Existence of Extreme Points
@user251257 I see; the horizontal asymptote is breaking it. Can I still salvage it by requiring that $f (S) $ also be closed?
Jul
20
comment Hestenes' Existence of Extreme Points
Take $f(x)=x^2$ on $S=(0,\infty)$. Then $\inf_Sf=0$, but there exists no $x_0\in S$ such that $f(x_0)=0$.
Jun
15
comment How are basis elements also elements of the topology?
+1 It follows by definition. For some reason I thought that I had to demonstrate it.
Apr
24
comment Continuity Rewritten: $\forall\delta>0,\exists\varepsilon>0\dots$
@BarryCipra, my diction was off: I meant to express "subtle," not "succinct." Thank you.
Apr
24
comment Continuity Rewritten: $\forall\delta>0,\exists\varepsilon>0\dots$
An implication is indeed not always equivalent to its converse. For this particular case, however, it was not readily obvious to me.
Apr
9
comment Converge the sequence $\left(\left(1+\frac{1}{n}\right) \left(1+\frac{2}{n}\right)\cdots\left(1+\frac{n}{n}\right)\right)^{1/n}$
It looks like you applied the natural logarithm (and its rules) to the above expression to end up with a Riemann sum. Is this correct?
Feb
19
comment Precise definition of limit
@Valentino: oh, man, I have that book, and it is not that straightforward. :-O
Feb
19
comment Probability and dice rolls
+1 I programmed a simulation that corroborates this.
Feb
19
comment Intervals of Convex and Concave function
You correctly found the point where the second derivative of the function changes its sign. Now, what you call each half is irrelevant, really. However, if rain falls from above, then $x>\ln1/2$ will collect water because it is concave.
Dec
10
comment
@Bak1139, are you familiar with clicking users' profiles to deduce whether they know how the system works?
Nov
28
comment Bipartite Graph and Non-connected node?
Do you know what it means for a graph to be bipartite?
Nov
28
comment Naturality of $n$-truncation
Please fix the title of your question.
Nov
27
comment Derivation of Simple Projectile Motion with Drag
I see. So I have to treat the components individually.
Nov
21
comment Prisoners Problem
To execute a finite number of prisoners, a strategy must be construed in such a way that after the execution of prisoner $m$, all successive prisoners guess the color of their hats correctly.