scapp

5 ms·

1.
by scapp 2mo ago
That's a different meaning of the word "undecidable". You're talking about undecidable problems [1]. The meaning in Gödel's incompleteness theorem is different and is a synonym with independent [2]. [1] https:&#x2F
2.
by scapp 3mo ago
Hmmm, it could definitely be clearer. It looks like it's using the bulk density for "sugar" (so including the air between the crystals) and the actual density for "sucrose".
3.
by scapp 4mo ago
It's somewhat a coincidence. In the paper, the dimension has to be larger than this constant K which is shown to be no larger than 1728. This is a fairly crude estimate that comes from multiplying a bunch of small numbers together, so
4.
by scapp 8mo ago
This is the easiest of the paradoxes mentioned in this thread to explain. I want to emphasize that this proof uses the technique of "Assume P, derive contradiction, therefore not P". This kind of proof relies on knowing what the r
5.
by scapp 2y ago
M.A. was the highest degree available in the UK at the time [1]. The closest equivalent to a PhD program might be the Prize Fellowship that Hardy had from 1900 to 1906, though it's certainly not one to one. Don't get the impressio
6.
by scapp 2y ago
Nothing wrong with starting at 1 for induction, but yes, having an additive monoid is nice (still get a multiplicative monoid with N*)
7.
by scapp 2y ago
*Bill Odenkirk. Bob is his brother
8.
by scapp 2y ago
Nice! I wondered if someone would beat that TAS level anyway.
9.
by scapp 2y ago
It's easy to find the UUID associated to a nickname. For example, here's [0] the one for `accrual` [0] https://namemc.com/profile/Accrual.1
10.
by scapp 3y ago
It's always fun to make fun of cranks. Thanks for linking that. The author really needs to find the right statement of what they call the Nested Interval Theorem. I cracked up at the complete misuse of it in the "Interval Argument
11.
by scapp 3y ago
Kind of disappointing that it doesn't have the victory screen. But man, my fingers still remember that combo you have to do for those 4 wide areas.
12.
by scapp 3y ago
2 line explanation of where e comes from here: to represent a number x in base b, you need roughly log_b(x) digits. If you weight that by the number of different digits in base b, you get b * log_b(x) = b * log(x)/log(b) = b/log(b
13.
by scapp 3y ago
> Last time I checked there was still no formal version of Cantor's diagonalization argument. Formalization? Like a computer checked proof? Lean: https://leanprover-community.github.io/mathlib_docs/logic/fu
14.
by scapp 4y ago
Check out the replies to this comment [1] with the same attempted counterexample. Your set isn't union closed because {1}U{2} = {1, 2} isn't in it (same for {1}U{3} etc.). [1] https://news.ycombinator.com/item?id=3
15.
by scapp 4y ago
There's a way to make it always appear above other windows. Let me see if I can find that again... Ah, it's in the options menu on the task manager itself (alt + O to access the menu without a mouse).
16.
by scapp 4y ago
I don't see the problem. For example, if something finishes in 10 minutes, it has 6 completions per hour. If a competitor finishes in 1 minute, it has 60 completions per hour. It both finishes in 1/10 of the time (time per complet
17.
by scapp 4y ago
> along with the other axioms the the theory is derived from Axioms are trivially provable in any system. Unless you mean prove them without using them, in which case you're actually talking about a system where they aren't axi
18.
by scapp 4y ago
> the unnameable reals, which are almost every real Is there a definition you have in mind for "unnameable"? If you mean definable [0][1], then this is independent of ZFC. The "standard" argument for this is flawed, a
19.
by scapp 4y ago
It's because the cone cells connected to those variants of colorblindness have very similar sensitivities to wavelengths. Check out this diagram: https://en.wikipedia.org/wiki/Cone_cell#/media/File:Cone-f
20.
by scapp 4y ago
Spaces like this (manifolds) are usually classified by which Euclidean space they look like locally. So, for example, the surface of a sphere is two-dimensional since it locally looks like a plane (whence flat-earthers). A two-dimensional t
21.
by scapp 4y ago
Maybe it's changed now, but the "π" in the title is unicode U+03C0 [0], which is a lowercase pi. In the font Verdana (the one that I see in the title, but not this comment as I type it[1]), U+03C0 looks like a small capital p
22.
by scapp 4y ago
Does this project still exist somewhere other than Google Code? It seems everything on the website 404s. EDIT: this might be it: https://github.com/Tipoca/intuitionistic
23.
by scapp 4y ago
The better term to use here is Socratic dialogue [0]. [0] https://en.wikipedia.org/wiki/Socratic_dialogue
24.
by scapp 4y ago
First, a point of terminology: uncountably infinite refers to any infinite cardinality other than countably infinite, so if the number of probability distributions is at least the cardinality of the real numbers, then it's already unco
25.
by scapp 5y ago
Wait, is there something wrong with the paper you linked? Theorem 1.1 says > There is an integer multiplication algorithm achieving M(n) = O(n log n). You don't call something a theorem if it's a conjecture.
26.
by scapp 5y ago
In case anyone's curious, the SCOTUS case was Kirtsaeng v. John Wiley & Sons, Inc. https://www.scotusblog.com/case-files/cases/kirtsaeng-v-john...
27.
by scapp 5y ago
I don't know what proof is used here, but the standard proof uses univalence to upgrade the equivalence (_ + 1): Z -> Z to a path Z = Z. Then we use induction for S^1 to define the map S^1 -> U that takes the base point to Z and
28.
by scapp 5y ago
Lean 3 introduced singleton-elimination which is inconsistent with HoTT. There's a project [0] that uses an attribute to restrict uses of that rule, but it isn't really ergonomic to use. [0] https://github.com/gebn
29.
by scapp 5y ago
I think they meant > Thus if you assume that the function is total and thus does halt, it must run in O(1) time. Since that's what total means.
30.
by scapp 5y ago
Problem 1: 1/(2^aleph_0) isn't a real number. The real numbers don't contain infinitesimals. It's possible to formalize a number that behaves like 1/(2^aleph_0) "ought to" (surreals would be one possible a

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