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If you solve this I'd award you with 500rep


May
2
comment Showing that $\|f\|_p\to\|f\|_{\infty}$
Many times indeed. Click in here and then look at the Linked column
May
1
comment image of intersections of sets and equality with intersection of images.
If you only allow families with nonempty intersection then yes, it works for constant functions, but then it no longer is a characterization of injectivity.
May
1
comment image of intersections of sets and equality with intersection of images.
The equality in second statement is a characterization of injectivity.
May
1
revised image of intersections of sets and equality with intersection of images.
Formating. Removing a tag. The question is purely set theoretic.
May
1
comment How to prove that $\det\left[\pmatrix{u_1 & v_1\\ u_2 & v_2\\ u_3 & v_3}\pmatrix{s_1 & s_2 & s_3\\ t_1 & t_2 & t_3}\right]=0$?
And the same is true in general. If the product of two nonsquare matrices gives a square matrix it will never be invertible.
Apr
29
awarded  Favorite Question
Apr
22
revised Prove that $ x^n - y^n = (x-y) (x^{n-1}+x^{n-2}y\,+ \,\,…\,\,+ y^{n-1})$
edited title
Apr
20
revised Finding Distinct Elements and Permutation in Partitioned Set
edit according to OP confirmation
Apr
20
comment Finding Distinct Elements and Permutation in Partitioned Set
Shouldn't it be "$x_i\in A_i\cap B_{\pi(i)}$"?
Apr
17
comment Hi I was thinking about a problem and have a question:
I think this was asked before
Apr
15
comment How to find a primitive element of $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})$ over $\mathbb{Q}$?
In any case it would be a linear combination of $\sqrt 2,\ \sqrt 3,\ \sqrt 5$.
Apr
14
comment why do we take this partition?
@mathse It means $\{0,\epsilon,1\}$ where $\epsilon\in(0,1)$.
Apr
11
comment $I=\mathbb{R}\backslash\{0\}=\left(-\infty, 0\right)\cup\left(0, +\infty\right)$? And why $-\dfrac{1}{x}$ is not increasing in $I$?
For the second question, no.
Apr
11
comment How can I prove that this function is a bijection?
Rewrite what Chinese reminder theorem says using your notation, that is with $[\cdot]_a,\ [\cdot]_b,\ [\cdot]_{ab}$.
Apr
11
comment How can I prove that this function is a bijection?
Okay, Have you hear about Chinese reminder theorem?
Apr
11
comment How can I prove that this function is a bijection?
For any $a,\ b$?
Apr
11
comment How can i show that $\det(A)=\det(A^\intercal)$?
Yes, by induction (strong induction). For $n=1$, it's clear. Then assume it holds for square matrix of dimension $1,\ldots,n$. You have to prove it holds for $(n+1)\times (n+1)$ matrices. You need a previous result that says that it's the same to expand a determinant, using minors, across any row or any column.
Apr
11
revised Question about finding where the function increases and decreases on $f(x)=\frac 1{x}$
added 2 characters in body
Apr
10
revised Prove that $ x^n - y^n = (x-y) (x^{n-1}+x^{n-2}y\,+ \,\,…\,\,+ y^{n-1})$
Some time passed since this was asked, enough to give the full solution.
Apr
6
revised Prove Matrix Power for 2x2 matrix using mathematical induction
added 6 characters in body