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Jul
11
comment Derivative that doesn't care about countable subsets?
@PhoemueX: No, I don't.
Jul
11
asked Derivative that doesn't care about countable subsets?
Jul
11
comment Notation: Set where function is positive
@BenWhitney: Why not simply $f^{-1}(\mathbb R^+)$?
Jul
11
comment Find all constants where a matrix is symmetric
Since the last equation reads $a+c=-2$, the lower right entry of your matrix should be $1$.
Jul
11
answered Why does the “separation of variables” method for DEs work?
Jul
11
comment Impossible numbers drawn from tricky function
Since the conditions explicitly exclude negative fractions, the question what "lowest terms" means for them is irrelevant for the definition of the function.
Jul
10
answered Equivalent definitions of an orthonormal function
Jul
9
comment What is the probability of picking a random number from 1 to 100, 100 times, and getting each number from 1 to 100?
Without replacement, the probability would of course be $1$.
Jul
9
answered Why is $0! = 1$ the same as $1! = 1$?
Jul
9
answered Manipulating sets ($+$, etc).
Jul
9
comment Manipulating sets ($+$, etc).
You mean, something like the fact that in general $A+(-1)A \ne \{0\}$?
Jul
8
comment composition of relations and multiset relations
@joriki: I wasn't aware of that. Interesting point.
Jul
8
comment composition of relations and multiset relations
@mathcounterexamples.net: If multisets are not sets, then functions are neither, because multisets are defined as functions.
Jul
8
asked composition of relations and multiset relations
Jul
8
comment Density of rational numbers
$\sqrt{2}-\left|p\right| < \sqrt{2}-p$ should read $\sqrt{2}-\left|p\right| \le \sqrt{2}-p$.
Jul
7
comment Why does mathematical convention deal so ineptly with multisets?
Maybe "inventory" would be a good name: For the inventory, you care about how many you have of each item, but not about any particular order (it doesn't matter if you have three bottles of water and two bottles of Coke, or two bottles of Coke and three bottles of water). Also, I think "subinventory" doesn't sound bad.
Jul
5
comment If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin?
Actually, an uniform prior means that you made no assumption at all about the fairness of the coin (you still get $p(Head)=0.5$ from ignorance: Since you have no bias, both results are equally likely). A prior 100% assumption that the coin was fair would mean $Pr(p)=\delta(p-0.5)$, and with that you'd find that the coin is fair with probability 1 no matter what you toss. Basically it's the "unshakeable belief" prior. In reality, you'd probably use a prior that's peaked around the fair coin (because most coins are approximately fair, but you wouldn't exclude the probability of it being biased).
Jul
5
comment Which of the following statements are correct?
@DerekHolt: OK, I've looked it up in the Wikipedia, and you're indeed right about the meaning of "order" (I consider that a useless definition since we already have a word for it, cardinality, and a confusing one, since "order" is already used for another notion in group theory).
Jul
5
comment Which of the following statements are correct?
@JonMarkPerry: Wrong in two ways: 1. Nowhere is stated that $x$ or $y$ may not be the identity element. 2. There are groups of order 2 that have more than 2 elements.
Jul
5
comment Which of the following statements are correct?
How do you get $x=y$ in case B?