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 Mar 2 awarded Curious Mar 1 asked Resolution of the $E_8$ singularity with a weighted blowup Jan 25 comment Normalization of the projective closure of affine plane curve over $\mathbb{C}$ Blowing up is definitely the way to go. For this problem you can dehomogenize at $\infty$, i.e. take $y=1$ and blow up by hand. This one will take more than 1 blowup. You'll get a local equation for the normalization this way. Jan 19 awarded Yearling Aug 14 comment If a line bundle admits a non-vanishing section then it is trivial If a function is nowhere zero then you can divide by that function Aug 11 comment How to calculate chained percentages? In these cases it is often easier to calculate the probability of you not winning. If you have probability $p$ of winning then you have probability $1-p$ of not winning. Your chances of winning within $n$ tries are one minus the chances of you not winning, i.e. $1 - (1-p)^n$. Aug 11 comment Does $F$ is an isomorphism $\implies F^{-1}$ is an isomorphism? In the category-theoretic sense, which is the sense you are asking, an isomorphism is a morphism $f:C \to D$ with a two-sided inverse $g:D \to C$. In particular, $g$ is also an isomorphism. In short: yes. Aug 11 comment Prove that there is an integer $k$ such that $x \lt k \lt y$. I think the "smallest" part is probably a typo. It should say largest in both cases. Now if $l$ is the largest integer less than $x$, then $l+1$ is an integer and is therefore larger than $x$ (otherwise $l+1$ is an integer less than $x$ but larger than $l$!) Jul 17 comment Definitions of $\mathcal{O}(n)$ and sheaves associated to a module @Hoot thank you for your response. I guess I should be able to show an isomorphism between the two definitions? I haven't thought it through fully... Jul 17 asked Definitions of $\mathcal{O}(n)$ and sheaves associated to a module Jul 14 comment Proper names for different representations of the same formula Formulas using the $\div$ symbol are incredibly rare because it's not associative (your example could be read $P\div (TVD \div 0.052)$ or $(P \div TVD) \div 0.052$, which mean different things) Jul 13 comment Mathematical Induction getting the right side What have you tried? Consider expanding... Jul 11 answered Proofs: Induction on Handshakes Jul 11 comment Questions about terminology (transpositions) $(2\, 4) = (1)(3)(2\, 4)$. Usually if an element is sent to itself then it is omitted in cycle notation. A transposition is a 2-cycle. A permutation containing a transposition that is not a 2-cycle looks like $(1\, 2\, 3)(4\, 5)$, which contains the transposition $(4\, 5)$. For your second question, $i$ denotes any number $1 \leq i \leq n-1$ if we are in the symmetric group $S_n$. Jul 10 answered Why does 0/0 mean there it a hole and not an asymptote? Jul 10 awarded Critic Jul 10 comment Find the Limit: $\lim_{x\to2^{+}}e^{3/2(2-x)}$ What is $\lim_{x \to 2^+} 3/(2(2-x))$? Jul 10 comment dim. of $\left[\mathbb{Q}\left(\sqrt[n]{a},\zeta_{n}\right):\mathbb{Q}\right]$ Do you know what the intermediate fields between $\mathbb{Q}$ and $\mathbb{Q}(\zeta_n)$ look like? Are any contained in $\mathbb{Q}(\sqrt[n]{a})$? Jul 10 comment dim. of $\left[\mathbb{Q}\left(\sqrt[n]{a},\zeta_{n}\right):\mathbb{Q}\right]$ Suppose $a \neq 1$. Can you write the $\mathbb{Q}(\sqrt[n]{a})$-minimal polynomial of $\zeta_n$? Jul 10 answered Minimal free resolution of the twisted cubic