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Apr
21
comment determine the closures of the set k={1/n| n is a positive integer}
Hi @Vikrant, if you are referring to the cofinite topology on $\mathbb{R}$, then yes, the closure of $k$ is $\mathbb{R}$.
Apr
20
answered What intuition do we have for a subalgebra of Lie to be abelian?
Apr
18
comment The number of choices of 3 kinds of crust and up to 6 distinct toppings
Do you know how many subsets (including the empty set) there are of a set with $n$ elements? (Hint: if you are stuck, think about this for small values of $n$ and try to identify a pattern; in order to write a formal proof, use combinations.) You can finish the problem by referring to Simon's comment.
Apr
5
revised Convolution of matrix coefficients is also a matrix coefficients
added 4 characters in body
Mar
23
answered Clarification on notation of “left invariant fields” (Lie groups)
Mar
20
answered Convolution of matrix coefficients is also a matrix coefficients
Mar
20
answered The closure of A is closed in X
Mar
12
comment Using the associativity of matrix multiplication to prove that if A^2015 is invertible, then A is also invertible
Hi @Lauren, in fact, if $AB$ is invertible for any matrix $B$, then $A$ must be invertible. Can you see why this more general statement is true? What definitions of "invertible" do you know (you can use the "determinant non-zero" definition, but any definition will work)?
Mar
3
comment Lebesgue Measure: show that a subset of R is equal to R
Hi @Martín-Blas, sorry, I didn't notice that condition. Thanks for the clarification!
Mar
3
comment Lebesgue Measure: show that a subset of R is equal to R
Hi @Sai, I'm not sure I understand - the condition you have is that $B$ is closed under addition, and certainly $B=\mathbb{Q}$ is closed under addition. Do you mean that the condition should be "$B'$ is closed under addition"?
Mar
3
comment Lebesgue Measure: show that a subset of R is equal to R
Hi Sai, what is $B'$? If $B'$ is the complement of $B$, then this is false and $\mathbb{Q}$ provides a counterexample. If $B'$ is the set of limit points of $B$, then the assertion cannot be correct either as this set is all of $\mathbb{R}$ if $B=\mathbb{R}$. Do I misunderstand the problem?
Mar
1
awarded  Necromancer
Feb
25
comment GRE Mathematics Practice Exams
Hi Uzman, in addition to @Peter's suggestion, there are also some practice tests available online at wmich.edu/mathclub/gre.html. However, and I think this is claimed on the website too, a few of the practice tests on this website are dated (when the exam was considered to be easier and not as good at discriminating between the best students). Also, you can buy some test preparation books on the mathematics subject GRE, and they could also serve as a useful resource. (I assume you are not referring to the mathematics portion of the General GRE; there are many resources for that!)
Feb
18
awarded  Enlightened
Feb
18
awarded  Nice Answer
Jan
13
comment A complex integration arround the boundary of a rectangular region
If you combine Green's theorem with your observation that the integral in question is $\int_{C} -dv$, then ...
Jan
4
awarded  Great Answer
Dec
23
comment Existence of complex polynomial with modulus on $|z|=1$ less than 1
More generally, you could also take $P(z)=a_0+a_1z+\cdots+a_nz^n$ for $a_0,a_1,\dots,a_n\in\mathbb{C}$ such that $\left|a_0\right|+\left|a_1\right|+\cdots+\left|a_n\right|<1$.
Dec
23
comment Existence of complex polynomial with modulus on $|z|=1$ less than 1
What about $P(z)=cz$ for any $c\in \mathbb{C}$ with $\left|c\right|<1$?
Dec
19
awarded  Constituent