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Nov
21
comment Are all the finite dimensional vector spaces with a metric isometric to $\mathbb R^n$
When you ask questions like these, always make sure all the different properties are tied together. You should have easily spotted the problem from the fact that you're talking about "finite dimensional vector spaces with a metric" - but a metric doesn't care about the vetor space structure, so the requirement that your set be a vector space is immediately forgotten.
Nov
18
comment Most ambiguous and inconsistent phrases and notations in maths
This is the one abuse of notation that I refuse to take part in. Many of the ones mentioned by Git Gud can genuinely simplify your writing, but is it really so hard to just write $(\sin x)^2$? It's two parentheses!
Nov
16
comment If a,b,c are three distinct real numbers
@Integrator It actually won't... notice SE doesn't show accept rate anymore.
Nov
15
comment Extremely tough limit proof for f(x) and g(x)
@Amad27 It basically is, but replacing "$\epsilon$" with "$\epsilon/2$".
Nov
10
comment Subtracting Quarters of Squares Equals Multiply?!
@Johanna Huh? Of course it's a good proof. They's not starting off by assuming equality, they're showing that the first equation is equivalent to the last.
Nov
9
comment A thought on Ancient Math
I think this question is too broad. Can you at least specify a period and country?
Nov
5
comment Why does convergence in law not worry about points of discontinuity?
I guess the trouble is that this is basically a subjective question... to me it's not intuitively clear that $X_n\to X$, since as you say, their laws disagree for certain events.
Nov
5
comment Why does convergence in law not worry about points of discontinuity?
@sanjab Perhaps I should have mentioned that I don't really understand the point of the example. Given that $F_n(0)=0$ for all $0$ but $F(0)=1$, I would find it more natural to just conclude that there isn't convergence in law. I don't see how the example is supposed to motivate changing the definition.
Nov
4
comment $\pi$ normal to the base $10$
Well, because it's an immediate consequence of the definition of "normal". Are you sure that's the question you wanted to ask?
Nov
3
comment Examples of mathematical discoveries which were kept as a secret
@DavidRicherby I got unreasonably excited by the term "Differential cryptanalysis", thinking it was going to be some form of cipher breaking based somehow on real analysis...
Nov
3
comment Silly technical question about polynomials in Lagrange's “résolution algébrique”
The proof of that fact is in the very last sentence of my answer, which I just detailed a bit more.
Nov
2
comment What is the motivation/application of dual spaces and transposes?
Why is that a useful thing to define..?
Nov
1
comment What is the motivation/application of dual spaces and transposes?
I still don't understand why this is a useful concept, though.
Nov
1
comment What is the motivation/application of dual spaces and transposes?
What do you mean when you say that $L$ "determines" a map?
Oct
31
comment Minimizing $\mathbb E((X-m)^2)$
@NigelOvermars Do you have a reference for a proof?
Oct
29
comment Proof of the Principle of mathematical Induction
It's effectively an axiom. You can prove it in a formal framework like set theory, but that's not really a "proof" in the traditional sense.
Oct
28
comment Where have I used the assumption that $X\in L_2$?
@RobertIsrael Actually, I think it might be required in the next question, which is to use the above to prove Markov's and Chebyshev's inequalities. Would it be required there?
Oct
28
comment Is the limit of a sequence of random variables unique?
@the_candyman What does "unique with respect to a distribution" mean?
Oct
25
comment Is there a simpler approach to this application of Dominated Convergence?
I can't quite follow the substitutions yet, but I think this is definitely how we were intended to do it.
Oct
25
comment Bad at computations… but not math?
What exactly do you mean by computations? You say that calculus is "more about concepts" as though you just have to sit around thinking about curves - but there's a lot of rigorous proofs going on in the background that I would call computations, and that you need to be able to follow in order to say you really understand calculus. Are proofs "computations" in your sense?