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bio website elaboratescheme.wordpress.com
location United States
age 22
visits member for 1 year, 8 months
seen 2 days ago

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)


Jul
11
comment Existence of a boundary point
I would just choose $b = \sup\{z \in [0,1] : T(z) = 0\}$.
Jul
11
comment Hausdorff or weaklly hausdorff may apply
But $X$ need not be Hausdorff. Let $X = \mathbb{N}$ with a basis $U_n = \{2n,2n-1\}$
Jul
8
revised Borel Measurability of Certain Type of Function
added 13 characters in body
Jul
8
suggested suggested edit on Prove that $\det(M-I)=0$
Jul
8
comment Borel Measurability of Certain Type of Function
@Ian, this actually only proves upper semicontinuity; since $f^{-1}(a,\infty)$ is not necessarily open. (Although that doesn't mean the details are correct.) Thanks for the feedback
Jul
8
comment Borel Measurability of Certain Type of Function
Nevermind, I've got it now.
Jul
8
answered Borel Measurability of Certain Type of Function
Jul
8
comment Borel Measurability of Certain Type of Function
@DanielFischer, I'm still having some trouble. What was it that you had in mind?
Jul
7
comment Borel Measurability of Certain Type of Function
Thanks, @DanielFischer! I'll give that a go
Jul
7
asked Borel Measurability of Certain Type of Function
Jun
19
comment Almost Disjoint Uncountable Subgroups of $\mathbb{R}$
Ah, yes. I feel so silly now.
Jun
19
accepted Almost Disjoint Uncountable Subgroups of $\mathbb{R}$
Jun
19
asked Almost Disjoint Uncountable Subgroups of $\mathbb{R}$
May
6
revised Countability of Different Sets
replaced x with \times
May
6
suggested suggested edit on Countability of Different Sets
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.