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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
asked Where have I used the assumption that $X\in L_2$?
Oct
28
accepted Is the limit of a sequence of random variables unique?
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
28
asked Is the limit of a sequence of random variables unique?
Oct
26
answered Prove that $n! > n^5$
Oct
26
accepted Is there a simpler approach to this application of Dominated Convergence?
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
asked Is there a simpler approach to this application of Dominated Convergence?
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?
Oct
24
accepted Prove that $\mathcal B(\mathbb R)\times \mathcal B(\mathbb R)\subseteq \mathcal B (\mathbb R^2)$
Oct
24
comment Prove that $\mathcal B(\mathbb R)\times \mathcal B(\mathbb R)\subseteq \mathcal B (\mathbb R^2)$
What I mean is I don't understand the definition of $\mathcal D$. The semicolon and colon aren't how I usually write set definitions. Is it $\{A\in\mathcal B(\mathbb R) \mid (\forall O\in\mathcal O)\ A \times O \in\mathcal B(\mathbb R^2)\}$ ?
Oct
23
comment Prove that $\mathcal B(\mathbb R)\times \mathcal B(\mathbb R)\subseteq \mathcal B (\mathbb R^2)$
I don't quite understand your notation. What is $\mathcal D$? And what does $B(0, n)$ mean?
Oct
23
comment How do irrational numbers lie on the number line?
@anorton That should be an answer.
Oct
21
revised Are “almost all” graphs hamiltonian?
added 3 characters in body
Oct
19
comment The set $\mathbb{Z}$ is totally ordered
How are you defining $-$? I suppose $b-a$ means "the unique $x\in\mathbb N$, if it exists, such that $a+x=b$". In that case, it would be equivalent and probably simpler to define $a\leq b$ as $\exists x\in\mathbb N\ a+x=b$.
Oct
19
comment proving a sequence is increasing defined by a recurrence relation.
To be clear, you want to show that the sequence $b_n$ is increasing. It's meaningless to say a relation is increasing.
Oct
18
comment How to formalize proofs
You're implicitly assuming that if you increase either $a$ or $b$, then $a/b + b/a$ will increase (or at least not decrease). You need to prove that (assuming it's even true).
Oct
18
comment Prove that $\mathcal B(\mathbb R)\times \mathcal B(\mathbb R)\subseteq \mathcal B (\mathbb R^2)$
@saz Yes.${{}}$