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2h
comment Functions between metric spaces (and how they relate to closures of sets)
Yes. It has something to do with the fact that $X$ is not compact.
16h
answered Vanishing Integral of a differential form without using Stokes' Theorem
17h
comment Solve this system of nonlinear differential equations
The fraction can be simplified to a constant, namely $\frac{k_1}{k_2}$.
17h
revised Chance of drawing 4 red marbles out of a big bag.
added 428 characters in body
17h
comment Chance of drawing 4 red marbles out of a big bag.
Ah. I misunderstood the question. I thought it was done in stages. I will correct accordingly.
18h
comment Vanishing Integral of a differential form without using Stokes' Theorem
Why is a pullback of a $2$-form a $3$-form?
18h
answered Chance of drawing 4 red marbles out of a big bag.
18h
comment meaning of a dense subset
That has to depend on the property
18h
comment System of differential equation (Matrix form)
@Danny No. Multiplying $M^{-1}$ to the left of $K$ scales rows of $K$ according to the diagonal elements of $M^{-1}$. This will destroy the symmetry unless all diagonal elements of $M^{-1}$ are equal.
18h
comment Injectivity in the zero homology
And I believe your argument is very valid. I'm not sure what you're not sure about your argument :)
19h
comment Injectivity in the zero homology
I am not sure about the context, but what you wrote seems reasonable. (One exception is when $A \cap B = \varnothing$, but in such case the kernel of $i_*^A \oplus i_*^B$ is also obviously trivial.)
19h
answered System of differential equation (Matrix form)
19h
comment How to show the following function is Riemann Integrable
@Quality Oh. I completely forgot about the examples. I apologize for completely misunderstanding the problem.
1d
comment How to show the following function is Riemann Integrable
@Quality I just realize that I might have misunderstood the problem. If $n$ is fixed when you define $f_2$, then it is integrable. If the first case in the definition of $f_2$ means "for some positive integer $n$", then $f_2$ is not integrable. (Its integral will be $\infty$.) However, in either case, $f_2$ is NOT zero at all rational points.
1d
comment How to show the following function is Riemann Integrable
@Quality You do realize that even the accepted answer does not say that $f_2$ is integrable, right?
1d
comment The formula $\DeclareMathOperator{tr}{tr}\mathrm{adj}(A)=\tfrac{1}{2}[(\tr A)^2-\tr(A^2)]I_3-[\tr A]A+A^2$ for the adjoint of a $3\times 3$ matrix
@Travis You are right. I thought that was given by "Let $A$ be a square matrix of order $3$". I now realize that I misunderstood the terminology. I'll try to fix it then.
1d
reviewed Approve Linear Algebra - Transformations, image, kernel
1d
reviewed Approve let $\alpha \in \Bbb{R} $ and $\cos(\alpha \pi) = \frac{1}{3}$, prove $\alpha $ is irrational
1d
answered The formula $\DeclareMathOperator{tr}{tr}\mathrm{adj}(A)=\tfrac{1}{2}[(\tr A)^2-\tr(A^2)]I_3-[\tr A]A+A^2$ for the adjoint of a $3\times 3$ matrix
1d
comment Convergence of Sum of Random variable to another - Cantor function
I believe this sum always converges, not just almost surely. I'm not sure what you are asking.