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5h
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?
22h
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 $\{A\in\mathcal B(\mathbb R) \mid (\forall O\in\mathcal O)\ A \times O \in\mathcal B(\mathbb R^2)\}$ ?
1d
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?
1d
comment How do irrational numbers lie on the number line?
@anorton That should be an answer.
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
13
comment What is a “formal definition” of a set?
Could you provide more context? What is the exact formulation of the question?
Oct
8
comment Is there a geometrical definition of a tangent line?
Could you clarify what you mean by "one direction" and "other direction"?
Oct
3
comment Is $x^{1-\frac{1}{n}}+ (1-x)^{1-\frac{1}{n}}$ always irrational?
@Slade You're right - this started out as a proof that there are no counterexamples for $n>2$ of that specific type, and then I forgot what I was trying to do. There may be counterexamples of a more general form.
Oct
3
comment Is $x^{1-\frac{1}{n}}+ (1-x)^{1-\frac{1}{n}}$ always irrational?
@RossMillikan $(a+b)^n\neq a^n+a^b$
Sep
30
comment Prove (or disprove) this $\sum_{n=1}^{\infty}\dfrac{a_{n}}{n}$ is convergence?
Can't you just let $a=1$?
Sep
25
comment What is the meaning of “true”?
The answers here may be helpful.
Sep
25
comment Really advanced techniques of integration (definite or indefinite)
@NikosM. Monte Carlo does numerical integration, not symbolic.
Sep
23
comment Hard-to-put-together but easy-to-prove results
Maybe something like ${n \choose k} = {n-1 \choose k} + {n-1 \choose k-1}$? Once you think of the argument, it's simple and obvious, but thinking of the argument isn't entirely obvious if you're new to combinatorics. I still think this question is too vague, though.
Sep
22
comment Why doesn't the definition of the interior of a set depend on the dimension of the set
@KarthikUpadhya If you ask me to find the interior of a set, I need to know what topology you're using. In other words, you need to tell me explicitly what dimension to use.
Sep
18
comment Why does implicit differentiation work on non-functions?
+1 for keeping it simple and accessible.
Sep
17
comment Searching for analytical or topological proof(s) of the Cayley-Hamilton theorem
I think I remember seeing a proof in which the CHT was shown to hold for a dense set of matrices, and then extended by continuity. I think the dense set in question was the set of complex-diagonalizable matrices.
Sep
16
comment Explanation of Cauchy's root test / criterion
There are no similarities between Cauchy's criterion and his root test, other than that they're both named after Cauchy.