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Jul
3
comment Is the notorious $n^2 + n + 41$ prime generator the last of its type?
$6^2+6+55661$ is divisible by 53.
Jul
3
comment Prove that two non-bald residents of NYC have exactly the same number of hairs.
How many people are there in New York? What if they all had different numbers of hairs?
Jul
2
comment Is there a general solution to the water-bucket logic problem?
Also relevant: math.stackexchange.com/questions/645845/…
Jul
2
comment Is there a general solution to the water-bucket logic problem?
I think I can prove that any reasonable solution looks like the one there: the search space is a simple loop, and the only reasonable thing to do is to proceed around the outside of the loop until you reach the target position and win, or return to the start position, in which case winning is impossible. (Note the interesting invariant that in any minimal solution, at all times a bucket is full or a bucket is empty.) But I can't finish the proof before work; maybe later.
Jul
2
comment Is there a general solution to the water-bucket logic problem?
Relevant: Making the water gallon brainteaser rigorous
Jun
30
comment Why aren't all NP-complete problems strongly NP-complete, if any NP problem can be reduced to an NP-complete problem
@GregMartin I don't think those are relevant here. It seems that OP's terminology is strange; their "strongly NP-complete" seems to mean "NP-complete" (in the standard sense) and their "NP-complete" seems to mean "NP-hard" (in the standard sense).
Jun
28
comment Which is the largest power of natural number that can be evaluated by computers?
@parkhyeyoo They're great for playing Starcraft.
Jun
28
comment Which is the largest power of natural number that can be evaluated by computers?
True. For example, we can say that it is probably quite impossible to calculate $7^{10^{100}}$ since all the computers in the universe won't be able to store its digits.
Jun
27
comment What's the point of eta-conversion in lambda calculus?
@Trismegistos $A$ and $B$ are “observationally equivalent” if they “do” the same thing: that is, if $A x\equiv B x$ for every $x$. This is obviously no stronger than regular equivalence, and Henning Makholm's example shows that it is strictly weaker.
Jun
27
comment What's the point of eta-conversion in lambda calculus?
Relevant: Understanding η-conversion (Lambda Calculus)
Jun
27
comment A kind of reverse Church-Rosser
Yes. I had in mind some simple construction that doesn't look at the actual values of $M$ and $N$, and it can't be anything like that.
Jun
27
comment A kind of reverse Church-Rosser
No, that will never work, because it neglects the assumption that M and N are $\beta$-equivalent, and that assumption is required.
Jun
27
comment A kind of reverse Church-Rosser
It seems like it ought to be possible to find some form that reduces to $M$ in normal order and to $N$ in another order.
Jun
27
comment Is a continuous function $f : \mathbb{Q}\to\mathbb{Q}$ always bounded on a closed interval?
Mice and Wimple.
Jun
27
comment What type of equation is this? How to solve it?
You should realize that your answer can't be right because it doesn't involve $a$.
Jun
25
comment How many ways to put 8 rooks on the chessboard which satisfy…
You're right. I'm sorry for not reading carefully.
Jun
25
comment How many ways to put 8 rooks on the chessboard which satisfy…
possible duplicate of In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other?
Jun
20
comment I was wondering, shouldn't the fraction $\frac {-2}{-1}$ be less than 1?
OP has revised the question.
Jun
20
comment I was wondering, shouldn't the fraction $\frac {-2}{-1}$ be less than 1?
That's not a stupid question at all. It's a great question! Noticing a pattern, then noticing that it doesn't always apply, and then trying to understand the true pattern that does always apply--this is what mathematicians do.
Jun
18
comment A number root of two irreducible polynomials?
Maybe our definitions are different. Mine is that a polynomial is irreducible if it is not the product of two non-constant polynomials. Under this definition, all first-degree polynomials are irreducible.