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1d
comment Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?
@SaaqibMahmuud I can't find that anywhere, but in topology, all maps are continuous, always (unless there's some exercise showing you something that goes wrong if it's not continuous). All the theory builds on the assumption that all functions are continuous, so there might be some little detail where the assumption is used in my proof, but I can't find it.
2d
comment Why associativity $h \circ (g \circ f) = (h \circ g) \circ f$ is required in composition?
The whole point of category theory is to study sets-with-structure (topological spaces, groups, schemes, etc.) without ever referring to elements. Therefore, within category theory, there is no requirement that morphisms are functions. This leads to possible non-associativity of composition, which we want to avoid. Thus it is assumed as a category axiom.
Jul
3
answered Infinity xkcd style: can a turing machine exist?
Jul
3
comment Prove that two non-bald residents of NYC have exactly the same number of hairs.
You actually have to assume that there are more than $500,000$ people with hair on their head. But that's not very difficult, since you would only need that more than $5\%$ of the people of New York has hair in their heads, which seems like a safe assumption.
Jul
3
revised Given a binary number, how do we get the last decimal digit?
added 11 characters in body
Jul
2
comment How do I figure out a per square inch price?
How many square inches are there in a $24\times24$ inch print?
Jul
2
comment Are there any divisibility rules using 7?
I would add $10$ and $11$ to that list. Those aren't difficult. $8$ is actually trickier in my opinion.
Jul
2
comment Infinity xkcd style: can a turing machine exist?
Well, if the first row is infinite, she will never finish laying it down, so she will never get to row two.
Jul
2
comment $\mathbb{Z}$ is Euclidean domain
@Groups He's not using it, he's stating what he wants to prove. He proves it below, saying that $r$ is the minimal element of $W$.
Jul
2
comment Construction of a matrix over $ \{-1,0,1\} $
@Martigan Yes, $H$ and $Z$ might be completely unrelated, as I see it, except for the fourth point. So this is more of a combinatorics exercise than a linear algebra one.
Jul
2
comment Construction of a matrix over $ \{-1,0,1\} $
@Martigan The fourth point in the description of $H$, maybe? And it seems that if $Z$ is the zero matrix, you would have trouble finding $H$ so that point $4$ and the second part of $3$ holds simultaneously. Perhaps you mean $h_{ij} = 1 \implies z_{ij} \geq 0$?
Jul
2
answered Binomial Coefficient Computation by Dividing Consecutive Terms
Jul
1
comment Finite mapping $f : \mathbb R^2 \to \mathbb R$
@N.H. While you're technically correct, I think you're missing his point. We want the preimage of a disconnected set. Those are usually also disconnected, as long as the function is continuous. And a disconnected subset of $\Bbb R^2$ must have infinite complement.
Jul
1
revised How to find the value of $2g(1)+2f(1)-h(1)$?
deleted 5 characters in body
Jul
1
revised How to find the value of $2g(1)+2f(1)-h(1)$?
added 12 characters in body
Jul
1
comment What is the convex hull of $ \{t \to e^{-\lambda t} : \lambda >0\}? $
@user251792 the notation is fine, there's just several things it could mean. It doesn't hurt to be clear.
Jul
1
comment Surface area of a slightly deformed sphere
Find $dA$ expressed by $r, \theta, \phi, d\theta, d\phi$ and do a double integration?
Jul
1
comment For any $n$ positive integers ($n\geq 5$) exactly 3 or 4 of them are equal to each other modulo $2^m$ for some $m$
@CuriousGuest Let me rephrase: Would $1, 5, 9, 2, 3$ be valid for mod $4$?
Jun
30
comment What are the odds of getting certain results on a six dice throw?
Is $X,X,?,?,?,?$ the same as $?,X,?,?,X,?$, like in poker or yahtzee?
Jun
30
answered Does $A$ and $(A+I)^{-1}$ commute for positive operator $A$?