They keep digging that hole deeper
Reminds me of 2048 making a slightly worse clone of Threes and then releasing it for free.
I don't really query, but it's good enough at code generation to be occasionally useful. If it can spit out 100 lines of code that is generally reasonable, it's faster to adjust the generated code than to write it all from scratch. More generally, it's good for generating responses whose content and structure are easy to verify (like a question you already know the answer to), with the value being in the time saved rather than the content itself.
O notation has a precise definition. A function f : N -> R+ is said to be O(g(x)) (for some g : N -> R) if there exists a constant c so that f(n) <= cg(n) for all sufficiently large n. If f is bounded, then f is O(1).
Before I blocked the instance I had nothing but miserable interactions with Hexbear users, and it had nothing to do with political opinions.
It's required, but nontrivially so. It has been proven that ZF + dependent choice is consistent with the assumption that all sets of reals are Lebesgue measurable.
It depends on your velocity
"Measure" is meant in the specific sense of measure theory. The prototypical example is the Lebesgue measure, which generalizes the intuitive definition of length, area, volume, etc. to N-dimensional space.
As a pseudo definition, we may assume:
- The measure of a rectangle is its length times its width.
- The measure of the disjoint union of two sets is the sum of their measures.
In 2), we can relax the assumption that the two sets are disjoint slightly, as long as the overlap is small (e.g. two rectangles overlapping on an edge). This suggests a definition for the measure of any set: cover it with rectangles and sum their areas. For most sets, the cover will not be exact, i.e. some rectangles will lie partially outside the set, but these inexact covers can always be refined by subdividing the overhanging rectangles. The (Lebesgue) measure of a set is then defined as the greatest lower bound of all possible such approximations by rectangles.
There are 2 edge cases that quickly arise with this definition. One is the case of zero measure: naturally, a finite set of points has measure zero, since you can cover each point with a rectangle of arbitrarily small area, hence the greatest lower bound is 0. One can cover any countably infinite set with rectangles of area epsilon/n^(2) so that the sum can be made arbitrarily small, too. Even less intuitively, an uncountably infinite and topologically dense set of points can have measure 0 too, e.g. the Cantor set.
The other edge case is the unmeasurable set. Above, I mentioned a subdivision process and defined the measure as the limit of that process. I took for granted that the limit exists. Indeed, it is hard to imagine otherwise, and that is precisely because under reasonably intuitive axioms (ZF + dependent choice) it is consistent to assume the limit always exists. If you take the full axiom of choice, you may "construct" a counterexample, e.g. the Vitali set. The necessity of the axiom of choice in defining this set ensures that it is difficult to gain any geometric intuition about it. Suffice it to say that the set is both too "substantial" to have measure 0, yet too "fragmented" to have any positive measure, and is therefore not well behaved enough to have a measure at all.
By performing measure-preserving transformations to non-measurable sets and acting surprised when at the end of the day measure isn't preserved. I don't blame AC for that. AC only implies the existence of a non-measurable set, which is in itself not totally counter-intuitive.
The axiom of choice doesn't say one way or another whether the spectrum in "the standard order" (is there a standard definition of more/less gay?) is a well ordering, only that there is some well ordering.
There's a search field on the front page. The rest is blank because I used the (default) "exact match" option, so the rest of the page is (by random chance) filled with spaces. The search function presumably uses knowledge about the algorithm used to generate the pages to locate a given string in a reasonable amount of time, rather than naively looking through each page.
This already exists. https://libraryofbabel.info/
Your comment appears in page 241 of Volume 3, Shelf 4, Wall 4 of Hexagon: 0kdr8nz6w20ww0qkjaxezez7tei3yyg4453xjblflfxx0ygqgenvf1rqo7q3fskaw2trve3cihcrl6gja1bwwprudyp9hzip5jsljqlrc8b9ofmryole35cbirl79kzc9cv2bjpkd26kcdi9cxf1bbhmpmgyc0l1fxz81fsc0p878e6u2rc6dci6n0lv52ogqkvov5yokmhs3ahi89i1erq46nv7d0h3dp2ezbb1kxdz7b4k9rm9vl32glohfxmk2c4t1v5wblssk6abtzxdlhc6g00ytdyree9q4w43j8eh57j8j8d4ddrpoale93glnwoaqunj8j2uli4uqscjfwwh6xafh119s4mwkdxk5trcqhv7wlcphfmvkx97i5k54dntoyrogo51n5i23lsms7xmdkoznop6nbsphpbi0hpm6mq3tuzy1qb677yrk832anjas7jybzxvuhgox49bhi21xhvfu0ny27888wv76hbtpkfyv4s57ljmn9sinju3iuc6na2stn9qvm1vo5yb9ktz1lcbjp0q9102ugpft1f7ngdzmnzv6qomn7zfnopn02v9wwe2gr2m6mo0o9vjmrvmd7fp4kjivsy6iu9cfz9dyu6gv7542ujz0vtj7m2ifpnfeezrb2gbwbgkbdx2taq7vlgjedqze22ywsyt1cacfxxpftjumke4vbtvmn6skj3mi5qnprrv9w4pq5t23xlvrxufsmri2uljpw72228q6jvh82e6936400czpzs8w6i25dvgk7vgj9o9r3k4nombsl3iiv1cogggcw9e5non0jn9ni1aacbisa1oqlzgi9qyhmmd67hkxsfri5958cyj6ryou5vgz7uc7j9kkjix420ys1tkcrhgf0jm6la9h7e06z7sdijeiw31junshzgvmmpplqw6qbzzqzs39jictbygt8u6704h48hsc7hlffm513zagtdbfvpbz32r0vqmjz2sudta4gfsnx6ac4h76djsh7th2h4265qeeainsx2xgslfst5namazisk6swvsbpcv3osvr7wiabkh61f5vuxymqadzxilggym3kfqtbdl3xsmwqcr6wuf4gpoviog89h5xfyawlh7k79k9j5fn1wq47f1m73lah1qhfdxyt1pv2biean3jjb8qv0raxz1oxi9zs9tnmmwrhccd9fij39ddgn1g7t03norvzjqcbqbzl9ibq9qrksnutbfc47z2727u9d9tp68z7u2hyb805wy3d4d0ia9q50p4xvevryycogr6212tau2iv3ya0fy09rsh0wilpqj8vxqug9zj7h2ya1hbnapmqecwtbjnetmt2t91mhb7hky32tl3fa5dqtuba2hm5faawvkazugbmngeojzw88p6hl0duaiup166r20tubj16x78c5m73rwpecco5w6z8ti8b2pgof8k8vu99jvyqiaq6c6adybtjwi8i6u95efp1hxpdsvtbo6nm7j1lmv9jzdspp0sd3qk5jmfpfs1cy18euwpk0apiuqqdy7hakfjx83nx920p4ptxu6bsl98iywgdydrr54u6nvmyxwg1hd2vxnu2yq3utvbx5z886ezzblw0izmntai8jstisdju4n12eed5yr1avv9k7mrr9fzqs6zo7uc3ixkv6fz2figpb5tr1obrlf4c30ghf8exsdgwn1e0uo76r3klnqfys51extpnq5v5swql36lirgok8frxnntoywaqtmyzm3vclnnvfqohz56hh823k5d50049f3lye9cil24yk5031u27dpi7895319mkyi2pkpwxgay4fnqfj38emdc0990ezpheam8ab132v588je7ur4dv1wazezyokate2rccnii1y4gy4subra7y5of25xxu8s3mjumal1lypu1360mrzmqdqdfsm9lvmewzg1608hlxx4le00jhcowg7xcxsbhbx4swwze9pkyk0x8vpsr5j1yja5jl0wn8mjh3gh9wvszd2tazvj7fbuym2pee0r0ifsky61fulwloxc5jkon63tvarj5jsxg3kghl44e7o1w2deeboaodjpuvgzg82wrxszd5jk0hwhvaopdb8wcqqopob4mj2pn36yhnw6k6sz5y56xlijr5a4s6xmc68r0c20d7zq53mrjbq281nfkrrtqgnv2i2rag3f6ara9t616vovgqn8kjwrivene6yyskzxb0d4b0qy0aq743dptvxr85sfhqbcevkn17rvqv1l9hzx983cngckwhdu15kzdv10mqf8yibu0q8s3khd8d3fi5lbl9yespks1q1tnc4y1bgjtvyf1oppnxhvpou71olv0yapyq46w9ld0ntigpba6equ55fvs0j1tp7qw1hr8gbjz10gwxhsx3lu0hubgukht7mbkwfsu4x9980z1srfhj2ayw2e2xf2627vgctymfbooy4eythnm8nzr4mqnfycwovjvbyg95luo4h3smka9d3jlr7dn9e3xwwkpl4dg8i1mj7g63ludud8q7chfh4xajosfaps2n6ntye7j8o4lrcsbqas8ayiutyq8ckbn67ejioufkowogubs8o5670nz13bb9gq3obf0y9xq60j8n8d6i8ahzhxlj2rfc7ndsfmzhusihkiz9fdovslzad7in5kldzhqk8z0cua8n8l0vjfsy96qytgz4wgkq41h6rrsegy9yg1fqhnavpltd067gicomzhye6czk4voghysqscrwavw3li9qdj0ikrlwumyymf8n5luhz1orsrxfw1rek6ghsqyu486dfp2hkbilyccquihck0269nu8y7bsha503ax2ecpxjiug54viy229k4ienp6lcnyx03mnpadeslwa87mu6tcb7t3c3ug7g0yf5le9v2hp094n60ipetkyfu21vqxah8sjjmuhk1gzxnmz01o1s9ndefpfcat0vn1x1anypagcboxp515nmnj9f2yol1opdytfx2dmy5ypdpyamsp2p3zsegmd15e1jbo6xsznda92oqxo9kvsww9k1kzsuwjl73drq038uls6izgqzmhry879ctrhryaj750b2s3hus9f1ainad3vzphmataq0lkn7bi62pu0xf4uqb5k2o8656zn6vzilgl653t38y12723v193fe5c7vbv6p5lw5ernj7bl4aev1ccyakxmkwl11hot51pvrsvqd8vdptfq2ezq2jjaebwx
I'm not suggesting that. It just looks like he did in fact choose to have that hair color.
It looks dyed
I tend to agree, but I also don't see it as a fault of Linux/Arch. If you're not the sysadmin for your own system, who is? I'd rather do it, assisted by the collective knowledge of the community, than have Microsoft do it for me. For the last few years it's only required a handful of interventions, with the vast majority of time being spent on initial setup and (re) configuration rather than fixing bugs or addressing breaking changes. So IMO it's more of a test of your personal willingness to invest time into learning and building things than your ability to diagnose and solve technical issues.
That's not necessarily wrong, but not the big explaining factor here I think. The technological challenges behind aligning ML models with factual reality aren't solved, so it's not an engineering decision. It's more that AI is remarkably easy to market as being more capable than it is
Typst is pretty functional
Teen who ate spicy tortilla chip died of high chile consumption and had a heart defect, autopsy says
Jump
One definition of the complex numbers is the set of tuples (x, y) in R^(2) with the operations of addition: (a,b) + (c,d) = (a+c, b+d) and multiplication: (a,b) (c,d) = (ac - bd, ad + bc). Then defining i := (0,1) and identifying (x, 0) with the real number x, we can write (a,b) = a + bi.