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4h
reviewed Approve Help needed with Probability Question
4h
reviewed Close Are $\cos$ and $\sin$ linearly dependent in $[- π , π]$?
4h
comment A question in matrix norm
@Payton Do you mean a natural matrix norm? i.e. the matrix norm that's induced by its action on a vector norm? If so, then why specify $\|I \| \ge 1$ when $\|I \| = 1$ for any natural matrix norm?
4h
reviewed Close Why a graph $G=(V,E)$ has either one vertex $v\in V$ such that $\deg v\geq\sqrt n$ or all vertex has degree less that $\sqrt n$
4h
comment Local estimates for $|(x+\epsilon)^{-1} - x^{-1}|$
When $x$ is large, it is very easy to bound the difference. The only problem is when $x$ is very close to zero.
7h
comment Finding all primes $p$ such that $3p+20$ and $p+20 $ are primes
@AlexeyTsymbal If you need to find all such primes $p$, then it will take you a long time... Standard conjectures imply that there are infinitely many, but no one has proved this. Thus it is difficult to give any more transparent description than the one in the title.
7h
reviewed Reopen The intersection of dense subset and open subset
7h
comment How do I restrict k to ensure my matrix has exactly 3 distinct eigenvalues?
@SimonS Note that the question asks for more than just distinct roots, but distinct real roots. You can't discern that from just the gcd of the polynomial and its derivative.
7h
comment How do I restrict k to ensure my matrix has exactly 3 distinct eigenvalues?
1) Your question doesn't indicate any preference for exam-accessible tools. 2) Why don't you have access to it in an exam? 3) Are you saying you can factor cubic polynomials with ease? I think it would help if you clarify exactly what you are looking for. Do you want all values of $k$ or just some?
7h
comment How do I restrict k to ensure my matrix has exactly 3 distinct eigenvalues?
Well, instead of factoring you could use the discriminant of the cubic :). en.wikipedia.org/wiki/Cubic_function#The_nature_of_the_roots
7h
comment $A\subset f^{-1}(f(A))$ with equality if and only $f$ is injective.
@idm Strange, if you interpret $f^{-1}$ as "pre-image" then the $\subset$ should be $\supset$. The question makes slightly more sense if we interpret $f^{-1}(B)$ as "forward image of $B$ under some (prospective) inverse function $f^{-1}$". In any case you need to provide more context to make the question clear.
8h
revised What's wrong with this reasoning? (Cauchy integral theorem)
edited body
8h
answered What's wrong with this reasoning? (Cauchy integral theorem)
1d
comment Show that $P(x,y)=x^6+y^6$ is reducible over $\mathbb{R}$
I think you need another qualifier in your claim in the second paragraph: what about $f(x,y) = xy^4 + y^5$?
1d
comment Approximate summation of flooring function
Why not just use the exact value of $\sum_k \lfloor k/c \rfloor$? What's the context for needing to approximate it?
1d
reviewed Approve $n!+1$ being a perfect square
1d
reviewed Approve What is a theory and what is its extension
1d
reviewed Approve gauge-theory tag wiki excerpt
1d
reviewed Looks OK Sums of converging limits
1d
reviewed Leave Closed How to solve: $2x=(360÷4)$