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9h
comment What is the norm of the pre-multiplication by a fixed matrix operator?
That's a really interesting result!
9h
comment In how many ways can $1000000$ be expressed as a product of five distinct positive integers?
Have you verified your formula for the case $k=2$? I suspect you need to think carefully about exactly how you are defining $k$. Which value (or values) of $k$ does the factorization $(8,8,25,25,25)$ fall into? Or $(1,10,10,100,100)$? Doesn't seem like your $5\choose k$ term can account for both of these, but there's more than one way to organize these partitions and I'm not sure which one you intend.
1d
comment In how many ways can $1000000$ be expressed as a product of five distinct positive integers?
I was actually referring to the $4$ in your attempt ("five ones"). Note that there is at most one way to write any number as a product of five identical factors. This is a good indication that your formula $(\lfloor a/k \rfloor + 1) (\lfloor b/k\rfloor + 1) {5\choose k}$ is broken.
1d
comment Set that is bounded but not totally bounded: Reading textbook
It would be better to provide some detail to go along with the reference, as not everyone has access to the book, let alone that specific edition.
1d
revised Travelling salesman and NP Hard
added 53 characters in body
1d
comment In how many ways can $1000000$ be expressed as a product of five distinct positive integers?
This is not the only error, but how many ways are there to express $1000000$ as a product of five identical factors, really?
2d
comment Question on Furstenberg topology on Z and P subspace of primes
Thank you, this is a huge improvement! (downvote changed to upvote)
2d
comment (direct) sum vs span of subspaces
Yeah, the direct sum is also defined in terms of sums of finite subsets, so the two definitions are compatible. It depends a little on whether the OP really means direct sum. If the $U_i$ contain linear dependencies, I'd avoid calling it the direct sum of subspaces because it conflicts with the notion of direct sum of vector spaces. But it would still make sense to talk about their span.
2d
comment Question on Furstenberg topology on Z and P subspace of primes
Can you explain where you are stuck? Do you not understand the wording of the problem? Is there a particular term you are stuck with? What have you tried to look at so far? You really should give more details about what you're stuck with, right now your question reads as though you expect someone to provide a complete solution (because you don't indicate any effort on your part).
2d
comment Is the number of points on a plane larger than the number of points on a line?
You're aware that $\mathbb Z$ and $\mathbb Z^2$ have the same cardinality, right? "Surely adding an entirely new dimension..."
2d
comment (direct) sum vs span of subspaces
Would be nice to also address the case of $\{U_i : i \in I\}$ where $I$ is an infinite index set.
Apr
23
comment Prove that ${x^2+y^2=z^n}$ has a solution in $\mathbb{N}$ for all $n$ in $\mathbb{N}$
You magically jump from "$z^n$ is the radius of a circle" (the radius is in fact $\sqrt{z^n}$) to "Hence, $x^2+y^2 = z^n$ has a solution". That's not informal, that's just stating what you want to prove with no argument. Since when does a circle automatically have integer coordinates? (Hint: when $z=3$ it doesn't.)
Apr
22
reviewed Leave Open This one weird thing that bugs me about summation and the like
Apr
22
reviewed Close Logarithm : Finding unknown log base?
Apr
22
reviewed Leave Open Finding the limit of $\prod_{i=1}^\infty p_i$ with $p_i<1$
Apr
22
reviewed Leave Open Validity of a first-order formula
Apr
22
reviewed Close Iterative method for a positive definite matrix
Apr
22
reviewed Close Algorithms for generating a random $n$-element subset
Apr
22
reviewed Close Radius of convergence of the power series
Apr
22
reviewed Close Evaluating an integral using Gamma function