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Oct
23
awarded  Quorum
Oct
19
comment Questions related to maximal ideals
Well, I have seen a definition of a unity in a ring as a non-zero element, which means that the zero ring is then a ring without unity. I know this is strange, but it is exactly for the reason that zero ring is too weird to be a unit ring.
Oct
7
comment How do I find the following definite integral?
Mathematica forever? Not quite in this case :p
Oct
6
comment Fundamental Theorem of Calculus application
It would be wise not to use $x$ for two different variables, it is very confusing.
Oct
3
comment If $A$ is dense in $S$ and $S$ is dense in $T$ , then $A$ is dense in $T$
@KyleStrand Because \bar goes before A, not after that. There's actually a red nothing after the 2nd \bar showing that an argument is missing. The correct thingy is: $\bar S \subseteq \bar A$. And I get your point. Just somehow, you can change balls to "bubbles" (arbitrarily shaped open sets) and it's the same, still keeping the idea behind. And you can even draw it like that without any need of letters -- isn't that cool? :)
Oct
3
comment If $A$ is dense in $S$ and $S$ is dense in $T$ , then $A$ is dense in $T$
@KyleStrand The point is that you first derive that $S\subset \bar A$ implies $\bar S\subset \bar A$, which is a nice, simple and completely general statement, and is somehow the core of the proof. And now, you only use this very general statement, rather than fiddling with complicated stuff as $\epsilon-d(t,s)$, from which, no true idea can be observed.
Oct
2
comment If $A$ is dense in $S$ and $S$ is dense in $T$ , then $A$ is dense in $T$
@KyleStrand I don't like this because it assumes a metrizable space. And while direct and "elementary", it doesn't catch the points at all, IMHO.
Oct
1
awarded  Yearling
Sep
30
awarded  Explainer
Sep
29
comment Is the perimeter of a nested convex set smaller than the containing set's?
@Martín-BlasPérezPinilla Damn, my fault. Sorry for that.
Sep
20
comment Proof my by mathematical induction $\sum_{i=1}^{n} \frac{(-1)^{i-1}}{i} > 0 $
Hello, is really your summand independent of $i$? Because currently the sum evaluates to $(-1)^{n-1}$, which is not always positive...
Sep
19
comment Are $10\times 10$ matrices spanned by powers of a single matrix?
+1 Indeed a very nice proof by contradiction.
Sep
19
answered If A is a matrix, what does A' mean?
Sep
5
comment Can an observed event in fact be of zero probability?
@Did however, the question was on iid $[0,1]$.
Sep
5
comment Can an observed event in fact be of zero probability?
@Aahz No, the fact that you observed it once doesn't mean you'll observe it again later.
Aug
31
comment Why induction cannot be used for infinite sets?
Hello! Could you please tell us where the problem comes from and what have you tried to solve it?
Aug
31
comment Does the string of prime numbers contain all natural numbers?
I love that you have two solutions here: you show that every $k$ is a prefix of a prime written in the decimal system, the other answer shows that every $k$ is a suffix of it :)
Aug
23
comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins
Well, citing the question: Is there a way to do this without making use of a generation function?
Aug
23
comment Make $n$ cents with $1$-cent, $2$-cent, and $3$-cent coins
That still uses generating functions though, only simplifies the argument.
Aug
22
suggested rejected edit on If $A$ and $B$ are closed subsets of the set of real numbers, then is $A+B$ closed?