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Jun
30
answered Finding a cubic polynomial whose zeroes are the same as collectively of two other quadratic polynomials.
Jun
30
answered How to see a matrix presents a linear transformation?
Jun
30
comment When is $\lim_{b\to a} \int_a^b f(x)dx=\int_a^af(x)dx=0$
If the Riemann integrals in question are defined at all, ...
Jun
30
answered For $a\in\Bbb{R\setminus Q}$, is it possible to make $a(2n+1)\pi$ “almost” an integer?
Jun
30
comment Probability of two cot deaths in one family
The hypothesis of your third paragraph (a correlation between subsequence cot deaths due to - as of now unknown - common causes) would be worth an investigation with statistical means, but that would require thorough statistics about all cot cases with summaries (per family? per mother? with how many kids in total? per household?). For statistical significance one should test enough cases so that not to few cases of multiple cot are counted (at least 5, say). But if all such cases lead to a murder trial, it will be hard to obtain valid statistics ...
Jun
30
comment Probability of two cot deaths in one family
Even if we take the calculation for granted, we'd expect an event of two cot deaths in one out of 64 million pairs of children. So maybe Sally Clark is this one parent with two cot kids? Also, you say two of her children died? So the probability rises again ...
Jun
30
comment Proof that $a\equiv b \pmod n \iff a \pmod n = b\pmod n$
You cannot assume that $n\mid a$ and/or $n\mid b$. What are the exact definitions of the relation $\equiv_n$ and of the operator $\pmod n$ that aou are working with? Start by writing them down and staring at them a bit. - And your last staement $\exists x,y\colon\ldots$ is rather equivalent to $\gcd(a,n)\mid b$
Jun
29
comment Divisibility is not definable over $\mathbb{N}$ with coprimality relation
Simply swap $4$ and $8$.
Jun
29
answered hom and exact sequence
Jun
29
revised hom and exact sequence
added 238 characters in body
Jun
29
comment $K^\times$ isomorphic to $\mathbb{Z}/2n\mathbb{Z}$ when $K^\times$ is cyclic
What you show (or more generally: Every finite subgroup of $K^\times$ is cyclic) is not what is needed to be shown - we are given that $K^\times$ is cyclic. In other words, ruling out infinite fields is almost the complete task.
Jun
29
comment $K^\times$ isomorphic to $\mathbb{Z}/2n\mathbb{Z}$ when $K^\times$ is cyclic
@Roy $K^\times$ has one element less than $K$, so as I said it has $p^m-1$ elements, which is an even number, namely $2\cdot \frac{p^m-1}{2}$ as long as $p$ is odd.
Jun
29
comment Converting a set to a tuple?
Are you only considering finite sets of real numbers? Or more general situations?
Jun
29
comment How to find the integer part of big number?
It seems that $10^{10^{10}}$ could be the only answer that might be feasible to prove. But see below.
Jun
29
answered How to find the integer part of big number?
Jun
29
comment How to find the integer part of big number?
@cirpis $-10^{10}\ne (-10)^{10}$
Jun
29
awarded  Nice Answer
Jun
29
answered Matrix with rank 3 does not exist in this $p(x)$
Jun
29
comment what does secant mean in mathematics?
There's an image in Wikipedia
Jun
29
comment in statistics - why is type 1 error called type 1 and type 2 called type 2?
I agree that descriptive names like "false positive" and "false negative" would be preferable. There is no inherent order between the types of errors and it is hardly helpful if a) the author better lookup to make sure he doesn't mix things up, then b) the reader looks thing up to ensure he understands right and c) mst be afraid that the author might have nixed things up by forgetting to look up the definitions.