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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 Handsakes
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
Jul
10
comment Minimal free resolution of the twisted cubic
@TakumiMurayama Thanks! That did it. (I should say I computed the new sequence and it gives the correct result)
Jul
10
revised Minimal free resolution of the twisted cubic
edited body
Jul
10
asked Minimal free resolution of the twisted cubic
Jun
13
comment $S$ subring of $R$. Is a projective objects in $R$-$\bmod$ still projective in $S$-$\bmod$?
As another comment, $\mathbb{Q}$ is a flat $\mathbb{Z}$-module, which is maybe a helpful exercise