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Apr
6
comment Intuitive explanation for why $\left(1-\frac{1}{n}\right)^n \to \frac{1}{e}$
@xyz But the question wasn't why $e \neq 1$, it was how one limit can go to $e$ while the other goes to $e^{-1}$.
Mar
29
comment Real matrices with $n$ real positive eigenvalues, $A^2=B^2$. Prove that $A=B$
@Omnomnomnom But for your matrix, not all eigenvalues are positive...
Mar
7
comment How to show that $E[E[X\mid Y]\mid Y] = E[X\mid Y]$
Depends on how general your definition of the condition expectation is. What's your definition of $\mathbb{E}(X|Y)$?
Mar
6
comment Clarification on random variables?
@Teepeemm Uh, yes, of course. Fixed.
Mar
6
revised Clarification on random variables?
added 180 characters in body
Mar
6
revised How is it that 'if A then B' can be equivalent to 'A only if B'?
added 542 characters in body
Mar
5
answered How is it that 'if A then B' can be equivalent to 'A only if B'?
Mar
5
answered Clarification on random variables?
Mar
2
comment How do I find out if a multivariate function is multimodal?
Sample it at a few points, and see how it looks?
Feb
21
comment Find all analytic functions $f: E \to \mathbb{C}$ such that $z=(f(z))^n$ for all $z \in E$.
Hint: If $(f(z))^n = z$, then $f$ is the inverse of the map $x \to x^n$, i.e. the inverse of the $n$-th power operation. Any idea what that might be?
Feb
21
comment How is $\Bbb Z_0 = \{0, \pm m, \pm2m, \pm3m, \ldots\}$ denoted in set builder notation?
Fair enough, I just wanted to mention that there's a more direct way to express this
Feb
21
comment How is $\Bbb Z_0 = \{0, \pm m, \pm2m, \pm3m, \ldots\}$ denoted in set builder notation?
That's basically saying "$\mathbb{Z}_0$ contains all integers wich can be expressed as $km$ for some other integer $k$". While correct, that seems like a convoluted way of expressing $\mathbb{Z}_0$. Why not simply $\mathbb{Z}_0=\{\;km\;|\;k\in\mathbb{Z}\;\}$?
Feb
21
comment When do I solve a quadratic expression by either factorising, completing the square or use the quadratic formula?
In fact, completing the square may be viewed simply as a way to \emph{derive} the quadratic formula. It has the advantage that it doesn't require remembering any formulas, but at the cost of requring a few additional algebraic manipulations. Thus completing the square is usually favored over the quadratic formula by people who, like me, aren't good at learning things by heart.
Feb
19
answered Intuition behind the definition of a surface
Feb
19
answered Compute joint Probability Distribution of Three Random Variable when two joint PDFs of two r.v. are known
Feb
16
comment Is the probability of observing a specific event in a countably infinite set of events over countably infinte samples 1?
+1 for the connection to Kolmogorov's 0-1 law
Feb
14
revised Why if $\lim_{n \rightarrow \infty} f_n(x)=f(x)$ for all $x \in X$, we cannot directly say that $f(x)$ is the uniform limit of $f_n(x)$ as well?
deleted 41 characters in body
Feb
14
revised Why if $\lim_{n \rightarrow \infty} f_n(x)=f(x)$ for all $x \in X$, we cannot directly say that $f(x)$ is the uniform limit of $f_n(x)$ as well?
Fixed stupid typo
Feb
14
answered Why if $\lim_{n \rightarrow \infty} f_n(x)=f(x)$ for all $x \in X$, we cannot directly say that $f(x)$ is the uniform limit of $f_n(x)$ as well?
Feb
14
comment Is there a way to prove this exponential inequality?
Why is assuming that $a^b > b^b$ and that $a^a > a^b$ any more "basic" than assuming that $a^a > b^b$, I wonder?