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location Palo Alto, CA
age 24
visits member for 3 years, 7 months
seen 2 days ago

May
17
comment Is there a connection between uncountable sets and exponential growth?
Thanks. Should I close this question? (It doesn't really make sense anymore)
May
17
comment Is there a connection between uncountable sets and exponential growth?
Interesting... a few clarifications: (1) how did you formalize the notion of a "limit" here, (2) is there a concrete example of an element that's in the Cantor set but not in $C_n$ for any $n$, and (3) can you please give some more context for the last expression?
May
17
comment Baby Rudin 2.26 Infinite subsets with limit points implies compactness
+1, I also had trouble with this part of the problem, and your answer was extremely helpful. My original strategy was to write each $U \in \mathscr{U}$ as a union of $B \in \mathscr{B}$, and then show that the collection of all possible unions of $B \in \mathscr{B}$ is countable. Oops--this collection is actually uncountable.
May
4
comment 6 keys and a door( probabilities)
What have you tried so far? Can you break the problem down into smaller parts? Can you think of a simpler version of the problem that you can try solving first?
Aug
29
comment What's the probability that a sequence of coin flips never has twice as many heads as tails?
This solution is beautiful! One thing I don't understand is, how did you set boundary conditions for the region n >= 0?
Aug
27
comment What's the probability that a sequence of coin flips never has twice as many heads as tails?
Wow, incredible (both the write up and the result itself)! However, I have a slight point of confusion--why is S(1) = 1, rather than 3?
Aug
27
comment What's the probability that a sequence of coin flips never has twice as many heads as tails?
Sorry, I'm not sure I follow. Can you please explain what P(n) represents in slightly more detail?
Jul
10
comment Proving the countability of algebraic numbers
An alternative approach to showing that polynomials with integer coefficients are countable: consider the bijection $\phi: \mathbb{Z}[x] \rightarrow \mathbb{N}$ that sends the polynomial $a_0 + a_1x + a_2x^2 + \ldots + a_nx^n$ to the natural number $2^{b_0}3^{b_1}5^{b_2}\cdots p_n^{b_n}$ (notation: $p_i$ is the $i$-th prime number and $b_i$ is the image of $a_i$ under any bijection from the integers to the natural numbers).
Jul
9
comment Motivating linear algebra for economics students?
Why the -1? Anything I can do to improve this question?
Jun
29
comment Is there a “good” way to visualize complex vectors?
They are isomorphic as vector spaces over $\mathbb{R}$ only. But no, I was trying to figure out how you visualize 4 spatial dimensions in the first place.
Jun
28
comment Is there a “good” way to visualize complex vectors?
How do you like to visualize $\mathbb{R}^4$?
Jun
24
comment Are “$n$ by $n$ matrices with rank $k$” an affine algebraic variety?
Great answer, thank you! Regarding the definition, I agree with your disagreement; the book I'm reading explicitly says "this is only a temporary working definition" (the "real" definition to be given a bit later). Regarding the exercise, is there anything preventing me from taking the subspace spanned by the matrix with 1's in the first $k$ positions of the main diagonal? Finally, I'll try to get a handle on the geometric perspective in the meantime.
Jun
24
comment Are “$n$ by $n$ matrices with rank $k$” an affine algebraic variety?
Nice one, thanks!
Jun
12
comment Are cyclic groups always abelian?
Sounds good. And in fact, having this picture is great because it shows that each row (or column) is the previous row (or column) shifted by 1. What's more is that if we associate $e,a,b$ with $g^0, g^1, g^2$, then we can see the "addition table" structure come out.
Jun
12
comment Are cyclic groups always abelian?
This is a valid example, but giving a single example doesn't explain why we'd expect cyclic groups to be abelian in general.
Jun
12
comment How to find most negative number
@Abhijit As stated, this question seems to have a straightforward answer that doesn't require "Dual LPP". If this isn't what you're looking for, could you perhaps provide more context?
Jun
10
comment Contemporary Mathematical Columns in Magazines
I know these aren't columns, but do resources like TopCoder or Project Euler qualify?
Jun
10
comment How can I calculate the standard deviation knowing an event probability and a number of trials?
Good question! I hope it's okay that I removed the "probability-theory" tag.
Jun
10
comment Help with understanding and studying probability
And of course, posting such questions on this site would be helpful :)
Jun
10
comment Largest Part of a Random Weak Composition
That's a cool insight; if you actually use this approximation, what can you say about the error (especially when $n$ is small)?