Gabi Purcaru
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 Jul2 awarded Curious Dec10 comment $1/i=i$. I must be wrong but why? @arsmath that's why I said an not the Dec10 comment $1/i=i$. I must be wrong but why? my highschool math teacher told me to never use $\sqrt{-1}$; $i$ is just an imaginary number with the property that $i^2 = -1$. There's no such thing as the square root of a negative number. Aug28 accepted How to prove that $(X^a -1, X^b - 1) = X^{(a,b)}-1$ Aug28 comment How to prove that $(X^a -1, X^b - 1) = X^{(a,b)}-1$ this is so elegant, thank you! Aug28 asked How to prove that $(X^a -1, X^b - 1) = X^{(a,b)}-1$ Jun29 awarded Nice Question Mar18 awarded Yearling Dec16 comment How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? thanks for your input. I selected Hagen's answer because it describes all solutions though Dec16 accepted How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? Dec15 comment How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? $0 \in \mathbb{N}$, yes. Sorry for the confusion... This being my homework, I figured I was missing something, but now I'm starting to think the teacher was messing with us. Thanks! Dec15 awarded Commentator Dec15 comment How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? @Isomorphism I don't think that's the case, because $f(1^n) = f(1)$, not $f(1)^n$ Dec15 comment How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? @Isomorphism but isn't this just $f(x) = cx^0$ ? Anyway, I'm not convinced that these are the only morphisms either, because, for example, $f(0)=0$ and $\forall x > 0$, $f(x) = c$, or $f(0) = 8, f(1) = 2, f(2) = 4, f(x) = 8$ for any other $x$, etc. are valid morphisms. Dec15 comment How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? @Isomorphism can you give me an example for that? My reasoning is that if $x \mid a$ and $x \mid b$, then $x \mid a + b$, which means that $a+b = kx (k \in \mathbb{N})$. But then $(a+b)^r = (kx)^r = k^rx^r$ and $x^r \mid k^rx^r$. (I removed the other constant to make this simpler, it doesn't change anything) Is this wrong? Dec15 revised How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? edited body Dec15 asked How to find all morphisms from $(\mathbb{N}, \mid)$ to $(\mathbb{N}, \mid)$? Sep21 awarded Custodian Jul19 accepted Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$ Jul18 revised Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$ added 9 characters in body