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Oct
11
asked When does $a + b$ divide $a^p + b^p$?
Oct
11
asked Why does $a^n - b^n$ never divide $a^n + b^n$?
Aug
29
awarded  Good Question
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?
Aug
27
awarded  Nice Question
Aug
27
asked What's the probability that a sequence of coin flips never has twice as many heads as tails?
Aug
24
awarded  Nice Question
Aug
22
awarded  Enlightened
Aug
22
awarded  Nice Answer
Jul
30
awarded  Nice Question
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?
Jul
9
asked Motivating linear algebra for economics students?
Jul
7
awarded  Enlightened
Jul
5
awarded  Populist
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.