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2d
comment Show that 1 and -1 are the only eigenvectors of this linear transformation
$T$ is a linear operator on an $n^2$-dimensional space: its characteristic polynomial has degree $n^2$; in fact, it is $(x - 1)^{n(n+1)/2} (x + 1)^{n(n-1)/2}$. Your approach is fine, of course; you just have the wrong description.
May
25
comment Difficult Coordinate Geometry and Calculus Question
I haven't worked it out, but I bet it's easier to find the rectangle with the minimum area, and I would be unsurprised if it turns out to be square.
May
25
comment Difficult Coordinate Geometry and Calculus Question
In fact, you can easily see that every vertex can be $C$, by drawing a pair of perpendicular lines meeting $C$ and rotating them until they cut out chords of the same length. WLOG, let $C$ be in the first quadrant. If you start out with a horizontal-vertical pair, then the one chord has finite length and the other is "infinite". As you rotate it clockwise, the length of infinite one decreases to zero, and the length of the other chord increases.
May
25
revised Visualize $z+\frac{1}{z} \ge 2$
added 16 characters in body
May
25
revised Visualize $z+\frac{1}{z} \ge 2$
added 589 characters in body
May
25
revised Visualize $z+\frac{1}{z} \ge 2$
added 145 characters in body
May
25
answered Visualize $z+\frac{1}{z} \ge 2$
May
25
comment An introduction to algebraic topology from the categorical point of view
Filling in "on your own" isn't always so easy; language dictates how people think, and it isn't all that uncommon to see a text have tell you things about products, but remain silent about the corresponding statement for equalizers, so filling in the gap requires you to actually develop that part of the theory yourself (or discover relevant counterexamples on your own).
May
23
comment Integrating over the naturals. What does it mean?
Although note that, as a Lebesgue integral, this is only well-defined if the sum is absolutely convergent.
May
17
comment How to find cotangent?
@Severus: Doing things "inefficiently" doesn't give wrong answers. It looks to me like you computed $\cot(x)$ and $\cot(y)$ correctly; thus, the problem is either that you have the wrong formula for $\cot(x+y)$, or you made an arithmetic error when simplifying the result.
May
14
awarded  Enlightened
May
14
awarded  Nice Answer
May
13
comment Examples of methods for solving modular equations
@quapka: Huh, what an odd typo.
May
13
revised Examples of methods for solving modular equations
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May
12
comment Understanding the use of the Cartesian Product in the proof of $|\mathbb R\times \mathbb R|=|\mathbb R|$
The Cartesian product isn't producing a single element. It's the "interleave the digits" operation that is producing a single real number given two real numbers as inputs.
May
12
revised derivative with respect to $\log(x)$
added 55 characters in body
May
8
comment Is it possible to create a completely random integer between 1 and 13 using standard dice in a D&D dice kit?
@Amitai: because you'll have to discard 35% of rolls, rather than 2.5%.
May
6
comment How many ways can $133$ be written as sum of only $1s$ and $2s$
@Bliebervik: This is one of those things where it's obvious what he did if you know the technique, and you really shouldn't have any clue at all if you don't know the technique. (that said, the technique of using generating functions to count things is not, at least at a basic level, especially hard or complicated: it's merely thoroughly nonobvious)
May
4
revised Elements and arrows in a category.
added 793 characters in body
May
4
answered Elements and arrows in a category.