1,608 reputation
311
bio website elaboratescheme.wordpress.com
location United States
age 21
visits member for 1 year, 4 months
seen Apr 10 at 4:48

Undergraduate math major. Above (or to the side or below) is a link to my new blog where I'll be working my way through a number theory and algebraic geometry book. (And possibly coming here when I have frustrations.) Feel free to tune in their and give me your opinions! (Blog goes live on June 15th)


Nov
28
awarded  Yearling
Jun
21
comment Is there a difference between abstract vector spaces and vector spaces?
They should be the same thing.
Jun
21
comment A thought on that last term of an infinite sequence.
I'd recommend reading about the surreal numbers. The question you ask about $(0,1)$'s "greatest number" may be answered by looking at the surreal number $\alpha <(0,1)|1>$, which has the property that for any $x \in (0,1)$ $x < \alpha < 1$. On the other hand, the "least upper bound" for $\mathbb{N}$ would be $\omega =<\mathbb{N}|\emptyset>$
Jun
18
comment if $G$ is a group , $H$ is a subgroup of $G$ and $g\in G$ , Is it possible that $gHg^{-1} \subset H$?
This definitely doesn't hold for finite groups, since that map $\varphi_a: H \to H$ sending $x \mapsto a\cdot x$ is a bijection with inverse map $\varphi_{a^{-1}}$ defined analogously. Thus $|H| = |gHg^{-1}|$.
Jun
17
comment An integer $n$, such that $nx = 0$, where $x$ belongs to the quotient group $\Bbb Q/\Bbb Z$
A little more formally, In the above comment, I meant to construe that the binary group operation $+:G \times G \mapsto G$ leads to a well defined residue operation $+_H:G/H \times G/H \mapsto G/H$, and $+_H$ has the property that for any $a,b \in G$, $(a + b) + H = (a + H) +_H (b + H)$. So you may carry out the multiplication however you wish, and it remains an operation on $G/H$ no matter what.
Jun
17
comment An integer $n$, such that $nx = 0$, where $x$ belongs to the quotient group $\Bbb Q/\Bbb Z$
You're right up until $2x = \frac{2a}{b} + 2Z$. It's just $\frac{2a}{b} + Z$, since it's still a coset modulo $Z$, not a coset modulo $2Z$. So your thinking is correct in that $n$ is any (positive) multiple of $b$.
Jun
16
comment $G_1/H\cong G_2\implies G_1\cong H\times G_2$?
It's not generally true that the existence of a counterexample ensures the proposition fails in all cases. For instance, we have the naive example $e/e \simeq e \simeq e \times e$ where $e$ denotes the identity group.
Jun
16
comment Square root limit problem
@labbhattacharjee Jinx!
Jun
16
comment Square root limit problem
Right now it's very difficult to figure out what your question means... you should use $\LaTeX$ markup to make your question more readable
Jun
13
accepted Another Error in Neukirch's Algebraic Number Theory?
Jun
13
comment Another Error in Neukirch's Algebraic Number Theory?
I'll accept in a few minutes when it lets me.
Jun
13
comment Another Error in Neukirch's Algebraic Number Theory?
That makes so much more sense. I'm just so used to seeing "Every nonzero prime ideal..." that I completely missed the subtlety. Thanks!
Jun
13
asked Another Error in Neukirch's Algebraic Number Theory?
Jun
12
comment How would I go about finding a closed form solution for $g(x,n) = f(f(f(…(x))))$, $n$ times?
It seems like generating functions would help you out if you have a specific function $f$.
Jun
11
comment Clarification needed on finding last two digits of $9^{9^9}$
Oh okay, I had thought it said mod 10.
Jun
10
comment Sufficiently high power of a function is smooth
Ah okay, I've deleted my comment
Jun
10
comment Why do we write second derivatives like $\frac{d^2x}{dt^2}$
Also, it's always good to remember that sometimes we treat Leibniz's infinitesimals like quotients, but they really aren't.
Jun
10
comment How do I calculate how many push-ups will be done in a year, if I start with 1 a day, the first week, 2/day the second, etc?
Have you done any work so far?
Jun
10
answered Clarification needed on finding last two digits of $9^{9^9}$
Jun
9
awarded  Good Answer