81,365 reputation
4105205
bio website henning.makholm.net
location Copenhagen, Denmark
age 40
visits member for 2 years, 11 months
seen 3 hours ago

I'm a computer scientist by training (Ph.D. in programming language technology, 2003), currently working in industry. Real mathematics is more of a hobby.

In general, don't assume I necessarily know what I'm talking about, unless it's about computer science or formal logic. I dabble in various other fields that I've never taken courses in, mostly just by extrapolating from Wikipedia.


10h
answered Equation for the length of a chord parallel to either the minor or major axis in an ellipse
10h
comment Equation for the length of a chord parallel to either the minor or major axis in an ellipse
How are the chords you want to find the lenghts of specified?
10h
comment Uncomputability of subset relation
Hm, yes, right.
10h
comment Uncomputability of subset relation
Hm, what I see here are two general theorems: Let $D$ be some subset of $\mathbb N^{\mathbb N}$ such that there exists $f\in D$ such that every finite restriction of $f$ can extend to something outside $D$. Then (theorem 1) $D$ is not decidable when the input is an arbitrary function given as an oracle, and (theorem 2) $D$ is not decidable when the input is a total computable function given as a machine. Your examples all seem to fit as applications of these theorems. I don't think the proofs of theorems 1 and 2 feel very similar to me, apart from having the same premises.
10h
comment Uncomputability of subset relation
I'm afraid I still don't see any generic process for adapting one proof to the other here. All I can see are two proofs for two situations. Each proof is valid, of course, but I don't see how you think they are similar in strategy, much less systematically derived from each other.
11h
comment Uncomputability of subset relation
I accept that the diagonalizing proof in the edit works -- but it is not clear to me that it comes out of a systematic procedure applied to the oracle-based case. Indeed, I can't see that you ever use $A_1$ or $i_1$. You do say "let $i_1$ be any index for $A_1$", but neither $i_1$ nor $A_1$ appear anywhere in the rest of the proof ...
11h
comment What's a bi-rhombus?
Why not ask the teacher? The only occurrence of the word on the internet seems to be the three questions just asked here...
11h
comment Meaning of a bi-rhombus
@amWhy: math.stackexchange.com/questions/873413/what-is-a-bi-rhombus -- found by typing "bi-rhombus" into the MSE search box :-)
13h
comment Uncomputability of subset relation
I'm not sure how this proof would look if you converted it to work with indices, as you promise? How would you define $N$? A machine that gets $A$ as an index is not limited to query it for particular inputs; it can do all sort of static analysis on the input machine and try to prove general theorems about it. And even if you get an $N$, you can't expect that the machine will react identically to $A_1$ and $A_2$.
13h
comment Uncomputability of subset relation
@Carl: True -- I suppose the oracle interpretation didn't even occur to me here because it's so obvious that you can't decide the subset relation with finitely many oracle queries.
17h
comment Formal construction of $\mathbb Q$: interpretation and equality of elements
@NicolasLykkeIversen: Note that decimal expansions are not the defining characteristic of the reals (unless you're taking a rathet unusual path to them). It is true that every element of $\mathbb Z$ maps directly to the same real as the do if you map them via $\mathbb Q$, but being "the same real" is not a matter of its decimal expansions.
22h
awarded  probability
23h
comment sub-nanoseconds resolution
@ronexdicapriyo: I'm unsure what you're asking. If you have a number of 65536ths of nanoseconds, and want the same time interval in nanoseconds, divide that number by 65536. That's what "65536ths" means.
1d
revised sub-nanoseconds resolution
edited tags
1d
answered sub-nanoseconds resolution
1d
comment Proof that all ordered fields are in the Surreals
@JohnFernley: That must be because the surreal numbers are a proper class and so the NBG machinery is required to even speak about them as an object. However, NBG conservatively interprets ZFC, so if we can find a formulation without proper classes (e.g. define what a "subfield of the surreal numbers" is instead of the surreal numbers themselves), then this would be equally provable in ZFC.
1d
comment Reduced Row Echelon form without scalar multiplication?
@user3672888: Different texts seem to differ about whether (non-reduced) row echelon form requires the pivot elements to be 1 or not. If it does, then the same argument as here applies (with "triangular matrix with ones on the diagonal" instead of the identity). If not, then the usual Gaussian reduction will work -- just skip the pivot normalization steps.
1d
revised Restricting Binary Operator $*$ To A Subset
edited tags
1d
comment Does every triangle have a slope?
It is very unclear what you're trying to achieve here. Did you forget to describe the problem you're solving before you started writing about your solution?
1d
comment Square root of $\frac{2}{2^x}$; how do I find $x$?
Do you mean $9.313225746154785\times 10^{āˆ’10}$ instead of $9.313225746154785eāˆ’10$?