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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.${{}}$
Oct
18
asked Prove that $\mathcal B(\mathbb R)\times \mathcal B(\mathbb R)\subseteq \mathcal B (\mathbb R^2)$
Oct
18
revised Is there an introductory book on Genetic Sequencing Theory for mathematicians?
edited tags
Oct
18
answered Why isn't area under curve from 0 to infinity of $\frac{1}{x^2}$ equal to 3?
Oct
17
answered “Introducing something extra”
Oct
13
comment What is a “formal definition” of a set?
Could you provide more context? What is the exact formulation of the question?
Oct
12
answered Adjusting weight of a body of water by substituting part of it with a lighter liquid
Oct
10
accepted Is there a geometrical definition of a tangent line?
Oct
8
comment Is there a geometrical definition of a tangent line?
Could you clarify what you mean by "one direction" and "other direction"?