00:01:16 <esolangs> [[Brianfuck]] https://esolangs.org/w/index.php?diff=108897&oldid=61557 * Squidmanescape * (+88)

00:02:58 <esolangs> [[Broken Tape]] https://esolangs.org/w/index.php?diff=108898&oldid=101638 * Squidmanescape * (+79)

00:03:38 <esolangs> [[Broken Tape]] https://esolangs.org/w/index.php?diff=108899&oldid=108898 * Squidmanescape * (-1) Every time I don't check, I get an error, huh.

00:04:24 <esolangs> [[Bulgu]] https://esolangs.org/w/index.php?diff=108900&oldid=17374 * Squidmanescape * (+69)

00:04:40 <esolangs> [[Business Offers]] https://esolangs.org/w/index.php?diff=108901&oldid=101804 * Squidmanescape * (+9)

00:05:42 <esolangs> [[BuxRo]] https://esolangs.org/w/index.php?diff=108902&oldid=87983 * Squidmanescape * (+89)

00:06:00 <esolangs> [[C-trice]] https://esolangs.org/w/index.php?diff=108903&oldid=79425 * Squidmanescape * (+9)

00:07:53 <esolangs> [[CATHY]] https://esolangs.org/w/index.php?diff=108904&oldid=98952 * Squidmanescape * (+75)

00:08:36 <esolangs> [[C@/Lol.js]] https://esolangs.org/w/index.php?diff=108905&oldid=101436 * Squidmanescape * (+9)

00:10:09 <esolangs> [[CCS]] https://esolangs.org/w/index.php?diff=108906&oldid=46656 * Squidmanescape * (+23)

00:11:01 <esolangs> [[YoptaScript]] https://esolangs.org/w/index.php?diff=108907&oldid=89248 * Squidmanescape * (+9)

00:18:39 <esolangs> [[ELVM]] https://esolangs.org/w/index.php?diff=108908&oldid=96953 * Squidmanescape * (+29)

00:21:10 <esolangs> [[Turing (Joshop)]] https://esolangs.org/w/index.php?diff=108909&oldid=57571 * Squidmanescape * (+8)

00:22:41 <esolangs> [[Snek]] https://esolangs.org/w/index.php?diff=108910&oldid=84483 * Squidmanescape * (+84)

00:24:15 <esolangs> [[SIMPLE (the other one)]] https://esolangs.org/w/index.php?diff=108911&oldid=102012 * Squidmanescape * (+89)

00:25:52 <esolangs> [[Recursoin]] https://esolangs.org/w/index.php?diff=108912&oldid=57154 * Squidmanescape * (+24)

00:26:24 <esolangs> [[CES updates]] https://esolangs.org/w/index.php?diff=108913&oldid=81493 * Squidmanescape * (+29)

00:27:40 <esolangs> [[Cell]] https://esolangs.org/w/index.php?diff=108914&oldid=71304 * Squidmanescape * (+98)

00:29:16 <esolangs> [[Chinese]] https://esolangs.org/w/index.php?diff=108915&oldid=43720 * Squidmanescape * (+92)

02:50:53 <Sgeo> r/bing told me not to use Balanced. Precise gave a good answer: https://i.imgur.com/JyrVvnd.png

11:02:22 <esolangs> [[Decleq]] N https://esolangs.org/w/index.php?oldid=108916 * ChuckEsoteric08 * (+520) Created page with "{{Stub}} '''Decleq''' ('''Dec'''rement and jump if '''L'''ess or '''Eq'''ual to zero) is an [[OISC]] by [[User:ChuckEsoteric08]] inspired by [[P1eq]]. ==Command== a b c Means: <code>b=a-1</code> and jump to <code>c</code> if <code>b</code> is less or equal to zer

11:21:35 <esolangs> [[EsoBASIC]] https://esolangs.org/w/index.php?diff=108917&oldid=108824 * ChuckEsoteric08 * (+1809) Added deadfish interpeter

11:26:13 <esolangs> [[EsoInterpreters]] https://esolangs.org/w/index.php?diff=108918&oldid=108809 * ChuckEsoteric08 * (+426) Added deadfish interpeter in EsoBASIC

16:50:53 <Sgeo> Does f(a, b) = ln(e^a + e^b) have interesting properties? Want to wonder what the next step "below" addition is, if logs turn multiplication into addition, what do they turn addition into

16:53:55 <Sgeo> Doesn't seem to have an identity element, unless -infinity in the extended reals counts.

16:56:50 <ais523> it reminds me a bit of a hyperbolic function, but I think it's different enough to be its own thing

16:58:06 <ais523> and + and max are sometimes used to form a semiring in the same way that × and + are

16:59:21 <ais523> and max(a, -∞) = a, a + 0 = a, a + -∞ = -∞ so you have the identities correct as well

17:00:21 <ais523> so maybe max fits Sgeo's requirement for a "step below addition"? of course it doesn't quite work with logs in the same way

17:04:54 <Sgeo> I don't understand that limit for max (and the limit for a+b is a bit redundant, right?)

17:05:19 <ais523> Sgeo: basically, the higher x is, the closer an approximation log_x(x^a + x^b) is to max(a,b)

17:06:50 <Sgeo> I think I need to try to visualize that more... but it approaching max does make the whole identity-is-negative-infinity thing make sense

17:08:50 <ais523> and yes, the limit is redundant in the +/× case but that doesn't make it incorrect

17:13:03 <ais523> a good search term for information about max/+ as a substitute for +/× is "tropical semiring" but Wikipedia doesn't have much that's useful on the page directly, it's primarily just definitions

17:13:53 <ais523> because pretty much all the relevant identities are the same, if you can prove a statement about +/×, it also often happens that you can use the same proof to prove the same statement about max/+…

17:43:13 <esolangs> [[SSREPL]] N https://esolangs.org/w/index.php?oldid=108919 * ChuckEsoteric08 * (+832) Created page with "'''SSREPL'''('''S'''imple '''S'''tring-'''R'''ewriting '''E'''soteric '''P'''rogramming '''L'''anguage) is an esolang by [[User:ChuckEsoteric08]]. ==Specification== Initial value Data String is taken from user input. Line numbers are 1-indexed. There is only one i

17:44:52 <FireFly> isn't that log base -inf <=> max also analogous to norms, with the infinity norm being max too?

18:02:27 <esolangs> [[User:ChuckEsoteric08/Interpreters]] M https://esolangs.org/w/index.php?diff=108920&oldid=108811 * ChuckEsoteric08 * (+1)

19:50:01 <Sgeo> f(a, a) = ln(2*e^a) = ln 2 + a. So... almost like addition is repeated f() but not quite.

19:52:09 <Sgeo> Although weird to think of repeated beyond, 2, since I'm not sure if f(f(x, y) z) = the obvious way to define f(x, y, z) or not

19:53:28 <b_jonas> one step below addition is the successor operation, or, if you wish, a two-argument successor like succ(x,y) = 1+y

19:55:43 <b_jonas> because succ(y,succ(y,...succ(y,succ(y))...)) = x + y where you nest (x-1) succ operations, y+(y+...(y+(y+y))...) = x*y where you have (x-1) additions, y*(y*...(y*(y*y))...) = x↑y where you have (x-1) multiplications, and you define tetration similarly for natural numbers

19:58:14 <b_jonas> this is useful because this is actually one way how you can define addition of natural numbers, such as in Peano arithmetic

19:58:58 <b_jonas> (the alternative is to define cardinal addition from the union of two disjoint sets, and then restrict that to finite cardinalities)

20:05:58 <ais523> in Church numerals, addition is defined as (a+b)x = a(x) × b(x), so I think it's using the distributive law backwards?

20:07:58 <b_jonas> oh, the ln thing. that's based on how addition and multiplication relate, but not really on how they compare to exponentiation or tetration, so it's a different step backwards

20:08:39 <fungot> ais523: in that case, the government, although the bill to close the funding gap, to some, the most attractive place to do the investigation, the uk failed to see the point of.

20:10:29 <ais523> ooh, application is exponentiation in Church numerals, so the definition is actually x^(a+b) = x^a × x^b

20:10:57 <ais523> they basically define addition in terms of multiplication, exponentiation and logarithm

20:12:30 <ais523> (and because exponentiation is function application, you can define logarithm using lambda)

20:13:15 <ais523> or, hmm, I'm not sure that last comment is quite right, but it seems to be along the right lines at least

20:13:15 <b_jonas> what? why would you define addition in terms of multiplication and exponentiation? wouldn't you define it by applying one of the church numbers on succ and then applying that on the other number?

20:13:57 <ais523> hmm, we can compare the definitions I guess? the definition in terms of multiplication and exponentiation is (:)~*(~)*~*(*)*

20:15:11 <ais523> the former's much more efficient because you don't need to actually evaluate the number

20:15:28 <ais523> and I think it's the normal definition for Church numerals because successor itself is defined as addition of 1

22:44:07 <Sgeo> base sqrt(2) makes the addition as repeated whatever happen to work out, but I think it's a cheat. log_sqrt2 (sqrt2 ^ x + sqrt2^x) = log_sqrt2 (2) + log_sqrt2 (sqrt2^x) = 2 + x

22:44:34 <Sgeo> Having trouble telling Wolfram Alpha to do log base sqrt(2) of 2. It's interpreting it as