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1d
comment Why does tensoring a projective resolution with a flat module give another projective resolution?
Oh, I thought that you were allowed to used the fact from the linked thread. I may have misunderstood.
1d
comment Why does tensoring a projective resolution with a flat module give another projective resolution?
I think it's because tensoring with a flat module preserves exact sequences.
1d
comment I got the answer for $\lim \limits_{x \to \infty} {\left({3x-2 \over3x+4}\right)}^{3x+1}$, but only by a mistake - how do I solve correctly?
The derivative of $(3x - 2)(3x - 4)$ is not $(3)(3)$.
1d
reviewed Edit suggested edit on Derive a procedure to select one of the 2 options with equal probability when we are not using a fair coin.
1d
revised Derive a procedure to select one of the 2 options with equal probability when we are not using a fair coin.
TeXed
2d
answered Difficult first order ODE: $x't(x'+2)=x$
Jul
7
comment Fourier Transform-1
It would be helpful to show what you've come up with, and how you came up with it.
Jul
4
comment Rate of change of an infinite step function
I can try to come up with another notion, but I can tell you it may not be very useful because I don't know what you want to do with it afterwards. Here's my other guess. Suppose we pick some $p \ge 1$ and define $n_{x,\epsilon}(f) = \int_x^{x+\epsilon} |f(x)|^p dx$. I say that the limit of $f$ as $x \to \infty$ is a continuous function $g$ such that $\lim_{\epsilon\to 0} \lim_{x\to\infty} n_{x,\epsilon}(f - g) = 0$. (If you want the derivative, just put $g'$ instead.)
Jul
4
comment Finding the amount of numbers less than another number which are multiples of a set
The simplest idea that comes to my mind is the sieve of Eratosthenes. By the way, a multiple of a number and a factor of a number are very different. I believe you might want to use the word "multiple(s)" in your question.
Jul
4
comment Rate of change of an infinite step function
There are many ways you can say that. I think it depends on what you'll do with it afterwards. For example, you can say $\lim_{x \to \infty} \frac{f(2x) - f(x)}{x} = 1$.
Jul
4
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@Tim Again, I think you need to be more precise. Is there an example of something similar to what you might want?
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@Tim I think you need to be more precise. Would you accept $\det(A) = \int_0^1 \det(A) dx$? (I guess not.)
Jul
3
comment Proof of $|A^T|=|A|$
It is correct. Here's my attempt to elaborate. For a given $i$, let $j = \pi(i)$, so that $\sigma(j) = \sigma(\pi(i)) = i$ because $\sigma = \pi^{-1}$. It follows that $(\pi(i), i) = (j, \sigma(j))$. Since we define $j$ by $j = \pi(i)$ and $\pi$ is a bijection, each $a_{\pi(i), i}$ on the left-hand side of the equation matches with exactly one $a_{j,\sigma(j)}$ on the right-hand side.
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@Tim A matrix has finitely many elements. What kind of integration are you thinking about? What exactly is the thing you're looking for?
Jul
3
comment Matrices with the same characteristic polynomial
@Tim By the fundamental theorem of algebra, the characteristic polynomial is completely determined by its roots, which are eigenvalues (multiplicities included).
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
I think it depends on what you mean by "some kind of". In terms of linearity, the trace might be closer to "some kind of integral".
Jul
2
awarded  Curious
Jul
1
awarded  Pundit
Jul
1
revised What is the joint probability distribution of number of balls after $n$ draws?
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Jul
1
revised What is the joint probability distribution of number of balls after $n$ draws?
added 200 characters in body