The Nineteenth Byte

12:05 AM

2

easy mode of my previous challenge A perfect number is a positive integer whose sum of divisors (except itself) is equal to itself. E.g. 6 (1 + 2 + 3 = 6) and 28 (1 + 2 + 4 + 7 + 14 = 28) are perfect. A sublime number (OEIS A081357) is a positive integer whose count and sum of divisors (including...

cuz feed is slow

> ~-2**31
2147483647

Ginger

correct!

Radvylf Programs

@Bubbler Python? or something else

Bubbler

Yes python

Radvylf Programs

In JS that's a syntax error lol

I'm surprised Python allows that since it's usually pickier about disambiguity operator precedence than JS

I guess that's probably the fault of JS for not adding ** until like two years ago tho

Bubbler

unary minus being lower than ** just feels wrong to me :P

emanresu A

12:14 AM

→ 1 message moved to Trash

@JoKing would you mind unfreezing the bakery?

Jo King

@emanresuA done

att

12:46 AM

@Bubbler it's just multiplication ;)

lyxal

Thank goodness the second sublime number is a multiple of 64

Aiden Chow

@lyxal how u figure that out??

lyxal

Try it Online!

the number modulo 64 is 0

Aiden Chow

but it output 1 not 0

lyxal

because Ḋ is divisibility check

Bubbler

12:58 AM

@lyxal I showed its prime factorization there, and certainly 2^126 is a multiple of 2^6 :P

lyxal

Well see that wasn't immediately obvious to me :p

Aiden Chow

@Bubbler ok now that u say that, im face palm

OldSandboxPosts

Sandbox posts last active a week ago: Simplify a Cycle

Adam

1:15 AM

I was today years old when I learned that dict() and {} (in Python) are not identical

Bubbler

how

Adam

Each time you call dict(), it creates a new object in memory; each call to {} references the same object (I think, based on my experimentation)

onecompiler.com/python/3ye472qx9

Aiden Chow

@Adam huh thats interesting

Bubbler

I don't think so?

Aiden Chow

i find this too lol: doughellmann.com/posts/…

Bubbler

1:18 AM

That id is interesting but doesn't seem to reflect how it actually works

thejonymyster

@Bubbler sorry i misread the comment about there being "possibly more sublime numbers" i didnt consider the (hypothetical) odd ones

Jo King

a={};print(id(a)) seems to alternate ids

Adam

@Bubbler Yeah, I don't think that there's any actual implementation difference between them, but they function differently under the hood which I didn't expect

Bubbler

> 0.239us vs. 0.0407us - significant slowdown

Adam

@JoKing Hmmmmmmm, that's weird -- I guess that when you store the value in a variable, it always has to make a copy, whereas if you're referencing the value independently it can share memory???

The same exact thing occurs for non-empty sets and dictionaries

Aiden Chow

1:28 AM

@Bubbler yea, good thing i dont use dict() anyways :P

Adam

In order to understand this further, I would need to look through the Python source code, and I don't want to do that

Aiden Chow

bro u guys crazy enough to actually consider looking through python source code?!?!

like that thought has not even crossed my mind until u mentioned it lol

Adam

I mean, it's just C code, it's human-readable

Anyways, I learned this when trying to make a pseudorandom number generator without using random

Steffan

@Neil Right but that's not what it's doing here. It's returning . exactly every other time.

it acts the same way if you have files in the current directory. <*> does what you're describing.

Adam

1:46 AM

And I ended up with id(dict())%3%2 (since I'm trying to randomly get a binary value)

thejonymyster

@Steffan sorry i talk way better in chat than comments lol

Steffan

ok lol

Adam

@Steffan I know nothing about Perl, but from what I googled it seems that if you don't have any asterisks, then blobs don't return a list of files and instead work like the curly brace things in Unix shells which I can never remember the name of

EDIT: I realize now that the above claim is sort of obvious based on how Unix shells work, whoops
That would explain why `<.>` returns `.` instead of nothing; it doesn't explain why it returns nothing the other half of the time

Adam

2:15 AM

My best guess is that calling glob flips a flag somewhere which changes how it's parsed (e.g. then it only matches files that are just a period or something)?

All this has taught me is that I never want to use Perl

Number Basher

@Seggan designed to be easy to learn

Seggan

mm

forest

@Adam It's actually not that bad.

There are so many ways to do any given task in Perl, which is really nice.

I use "pure" Perl (i.e. no module support) sometimes on embedded devices, and it's not particularly painful.

Steffan

3:15 AM

@Adam Yeah, I already found out why it returns .. I just couldn't figure out why it's only half the time.

How I found this was by seeing a golfed solution lol

To determine whether the loop index was even.

also, this only happens inside of loops. outside of loops, it always returns the same thing.

Neil

5:46 AM

@Steffan well, yes, but think about what your glob is in your case

put it another way: suppose you've got a directory whose only file is a, then print while (<*>); will enumerate a and then stop; print(scalar(<*>)) while (1); will alternate between a and the empty string

emanresu A

6:02 AM

Fun puzzle game I found

att

6:26 AM

Any last-minute feedback/thoughts for codegolf.meta.stackexchange.com/a/24957 before I post?

Aiden Chow

@att cant understand any of it but it looks good!

Number Basher

6:45 AM

Suggestions welcome: (github.com/TvoozMagnificent/SunSip)

New Posts

7:22 AM

2

Q: Implement Level-Index Addition

Level-index is a system of representing numbers which has been proposed as an alternative to floating-point formats. It claims to virtually eliminate overflow (and underflow, in its symmetric form) from the vast majority of computations. The usual floating-point format internally represents a num...

code-golf restricted-time floating-point

Number Basher

0

A: Language nominations for the "Learn You a Lang for Great Good" chat event

SunSip This is a language I created myself. From the GitHub repo: SunSip, SLWNSNBP, or Simple Language Which Name Shall Not Be Pronounced, is a Turing Complete, Practical, Whitespace Insignificant, Simple programming language (which name shall not be pronouced). SunSip is based on variables, wit...

LYaL Nominations

7:48 AM

-1

A: Language nominations for the "Learn You a Lang for Great Good" chat event

SunSip This is a language I created myself. From the GitHub repo: SunSip, SLWNSNBP, or Simple Language Which Name Shall Not Be Pronounced, is a Turing Complete, Practical, Whitespace Insignificant, Simple programming language (which name shall not be pronouced). SunSip is based on variables, wit...

Aiden Chow

@LYaLNominations bruh rip it went from 0 to -1

Sandbox Posts

8:13 AM

0

A: Sandbox for Proposed Challenges

Debugger, Inspired by this challenge. Your goal is to write a function that takes in two strings and outputs a character. Yes. That's it. But the trick comes from the scoring. For every single character deletion, we will get an stdout (possibly empty) and an stderr (possibly empty). We then feed ...

Aiden Chow

any feedback (not posting yet but still): codegolf.meta.stackexchange.com/questions/2140/…

mousetail

8:42 AM

Why are all LOTM posts community wikis but not LYAL posts?

Jo King

8:55 AM

the general consensus seems to be ok with deleting the finished LYAL posts. does anyone have any last second objections?

i'd also like to add a list of completed ones to the actual post, so that users without permission to view deleted answers can see them too

emanresu A

I'll do that, you can do the deleting

~~speedruns flagging every single answer~~

Jo King

@NumberBasher already did that lol

well, 10 of them at least

Aiden Chow

@JoKing lmaooo

emanresu A

I'm doing it based on chat history so I can link to the events

So gimme fifteen minutes

Also, there are some without an announcement e.g. ><>, so I went with tthe next best thing:

Sep 14, 2021 at 23:39, by Jo King

so, we're doing ><> for LYAL?

Jo King

was Coconut the last one, i remember there being some discussion on it

emanresu A

9:05 AM

Honestly idk

Okay what

Nov 24, 2021 at 0:02, by caird coinheringaahing

Welcome to the seventh Learn You A Lang For Great Good! Today, we'll be learning Zsh, a Bourne Shell derivative that's used semi-frequently around the site. Feel free to ask questions about Zsh, post CMCs ("ZMC"s) related to the language, and just discuss the language in general. TIO.

Dec 22, 2021 at 0:00, by pxeger

Welcome to the ninth Learn You A Lang For Great Good! Today, we'll be learning zsh, a Bourne shell derivative that's (sometimes) good for golfing. Feel free to ask questions about Zsh, post CMCs ("ZMC"s) related to the language, and just discuss the language in general. ATO (or TIO, if you're so inclined)

Jo King

lol, double dipping

emanresu A

Oh wait #1 wasn't official

mousetail

That's not even far appart

emanresu A

was there even a seventh LYAL?

I'm just gonna roll with it

Jo King

has anyone titled their esolang the empty string? missing opportunity there

should be like Whitespace, but everything is zero-width characters

mousetail

9:11 AM

How would you even run it?

emanresu A

Feb 22 at 15:21, by Adám

@PyGamer0 I've reserved the empty string for my upcoming golfing language.

You've been ninja'd by six months lol

Jo King

./.py code

@emanresuA damn. foiled again by the immutable rule of dibs

emanresu A

Jan 19 at 0:12, by caird coinheringaahing

@lyxal vtc Vyxal as dupe of Perl :P

mousetail

@JoKing Wouldn't the name of the language be .py in that case?

emanresu A

Okay, the twelfth and thirteenth LYALs are void

Jo King

9:14 AM

@mousetail i wouldn't count extensions of the interpreter as part of the language name

(though i don't know if that would be a valid filename to call)

@emanresuA as in, we didn't learn a lang that week, but still counted it in the numbering scheme?

emanresu A

Honestly don't even know

It looks like they were respectively scala and maybe-dc

emanresu A

9:29 AM

Is it reasonable to say that LYALs have to have positive scores to be accepted?

Aiden Chow

@emanresuA ya that sound super reasonable

Number Basher

9:59 AM

+1

Um, I think we did-ish coconut, right?

thejonymyster

12:32 PM

@JoKing version two of this lang would make it ` 2`

Seggan

12:46 PM

@NumberBasher yeah

lyxal

come and gaze upon my horribly drawn graphs

thejonymyster

@lyxal please use software and fonts :-)

lyxal

gotta practice those hand-drawn graphs

thejonymyster

also i still dont understand why [1,2,7,2,7,2,3,7] => [1,2,3,7] and not [1,2,7]

lyxal

because it's not minifying the cycle

just making it simple

thejonymyster

1:01 PM

what property is preserved in 1,2,3,7, that isnt in 1,2,7?

(besides "the node 3" as youve already shown that some nodes can be removed lol)

lyxal

@thejonymyster the edge that connects 3 and 7

sure 1,2,7 is a cycle, but it isn't the same cycle simplified

thejonymyster

how do you determine whether it is the same cycle? what is significant about the 3<->7 edge that isnt significant about the 2<->3 edge or 3<->4 or 4<->2 edges in [1,2,3,4,2,5]?

lyxal

A cycle that visits all those edges between 2 and 7 is the same as one that only visits one of those edges

Radvylf Programs

Is the 2<->3 edge important?

lyxal

for this challenge, yes.

@thejonymyster the idea is that you're removing loops and parallel edges from the cycle, while maintaining the edges that aren't loops/parallel

@lyxal also, don't mind the fact I screwed up the drawing

thejonymyster

1:13 PM

so could [1,2,3,4,2,5] be either [1,2,5] or [2,3,4]

lyxal

no

New Posts

0

Q: All times of a wall clock in which arrows are x radians apart of each other

Take 12-hour regular wall clock with hour and minute arrow. Given x radians as an input - produce and return array of 24 elements, containing all possible valid minute and hour combination, where arrows are x radians apart of each other. (if x is a multiply of pi - then its 12 distinct values eac...

code-golf

lyxal

only [1,2,5]

can't be [2,3,4] because you've lost the first vertex after the start vertex

and the last vertex before the start vertex too for that matter

thejonymyster

ok, so this isnt some orderless set, the start and end (same point) of the path is significant, yes?

lyxal

> As the input represents a cycle, the vertex that is the start and end of the cycle will not be in the input.

thejonymyster

1:15 PM

ah right

the secret 0 point

lyxal

correct

well it's more assumed than secret

thejonymyster

right

i dont think it is very helpful to hide it in the input lol, it just makes it harder to see why it matters

lyxal

I was thinking it might help some algorithms out that might try and return the start/stop node

thejonymyster

i dont understand the difference between excluding 3 and 4 in the right graph, from excluding 3 in the left graph

lyxal

3 isn't excluded in the left graph

thejonymyster

1:20 PM

i know, but i dont understand why

to me its the same as excluding 3 and 4 from the right graph

lyxal

that's the definition I'm going off

thejonymyster

@lyxal this is incredibly dense :P

lyxal

@thejonymyster maybe this will help: 1,2,4,5,7,2,7,2,3,7 would also be 1,2,7,3

as would 1,2,7,2,3,7

and 1,2,7,4,2,7,2,3,7

I summarised it as "if a vertex appears twice, snip out the part in between the two appearances" in my notes from the lecture they taught this in

thejonymyster

that i can work with

but that math description is impenetrable

lyxal

I'm just going off what they said at the lyxture :p

thejonymyster

1:25 PM

lol fair enough

lyxal

excuse the highlight and annotations

that's the OG slide material

which I tried my best to paraphrase

thejonymyster

it seems more like you cut out important parts of it :P

like the part that includes v0

and how it equals vm and u

lyxal

isn't that a given seeing as how it's a challenge based on cycles?

thejonymyster

i... guess? it definitely seems like theres another ... in that second list though

but i digress

even just the "if a vertex appears twice, snip out the part in between the two appearances" would be nice to include

lyxal

done

thejonymyster

1:30 PM

oh also i guess maybe make it clear that youre not allowed to get rid of anything that isnt removed in this way

since its not about minifying, its about simplifying what is redundant

but yea thank you for taking the time to sit with me on this one i think i get it now :-)

lyxal

> Note that the simple cycle may not be the shortest cycle.

is that good or does it need a bit more?

@thejonymyster this is good for me too: it helps consolidate what I'm learning :p

thejonymyster

id add the reverse as well "and the shortest cycle may not be the simple cycle" ? :P

lyxal

also done

thejonymyster

its a good challenge btw i hope other ppl also understand it lol ^_^

~~now to close mspaint and go back to pretending to work~~

well now im curious what properties this simplified cycle has other than that it exists sfdg

like if youre studying it it must have some significance

am i gonna have to sit in on one of these lyxtures :-)

lyxal

It's a kind of guaranteed cycle

Unrelated String

1:43 PM

@lyxal wait wasn't that what i said in the comment you disputed

lyxal

@UnrelatedString probably is then

I'm new to this whole graph theory thing, so I may be a little smooth brain terminology-wise :p

CMQ: What's the default output rules for decision challenges?

pxeger

it's in the tag wiki IIRC

lyxal

is it enough to say "default decision problem output rules apply" or do I need to specify some criteria?

asking because it's been a while since I last wrote a decision problem

thejonymyster

i'm honestly not sure if you need to say it as long as you include the tag, but that would be enough yes :P

Number Basher

2:02 PM

@lyxal True. Consider a maximal connected subgraph of G, G'. There must be a maximal path in G'; WLOG let it be m~n. By the question, n has another neighbor, and as G' is a maximal path, the other neighbor of n is in G', z, and thus z-n~z (through the maximal path) is a cycle. Q.E.D.

lyxal

yes

my point was more that it was another example of a guaranteed cycle

thejonymyster

ough now i wanna think about graphs forever :-)

Number Basher

i remember there was also, a graph G with finitely many vertices each of degree ≥3 contains an even-lengthed cycle

thejonymyster

my brain just came across the (obvious) construction that any cycle can be extended by adding a vertex anywhere

and i dont know why but that is so awesome. love that

Number Basher

So maybe, for any n, a graph G (...) ≥ n+1 contains a cycle which length is divisible by n

who is willing to change the nineteenth byte into a MSE chatroom?

Anyways, let me see that question...

Sandbox Posts

2:06 PM

0

A: Sandbox for Proposed Challenges

Is This an Equivalence Relation? code-golf decision-problem Given a relation, and a domain, output whether the relation is an equivalence relation. Context For this challenge, a relation is defined as being a set of ordered pairs that is a subset of the cartesian product of a domain with itself. ...

lyxal

oh hey that's me

I wasn't expecting the X to be that far indented from the left :p

thejonymyster

seeing a latex issue in that post :P

Number Basher

There's too much math in code golf

1,654 questions has the tag math

lyxal

@thejonymyster huh, TIL MathJax requires matching brackets

Number Basher

About this, I think all implementations will use no math

at least most of the

m

mousetail

2:12 PM

Code golf is math though right? We're all collectively trying to find the algorithmic complexity of a problem, which we will be doing forever since it can be proved impossible

Number Basher

> algorithmic complexity

you don't know a thing about code golf, assuming you are talking about time complexity

mousetail

Algorithmic information theory

Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" (except for a constant that only depends on the chosen universal programming language) the relations or inequalities found in information theory. According to Gregory Chaitin, it is "the result of putting Shannon...

No, not asymptotic complexity, but information density

Number Basher

@lyxal

about this

1

A: Sandbox for Proposed Challenges

Simplify a Cycle code-golf graph-theory Given a path of vertices that form a cycle on a graph, output a simple version of the cycle. That is, if a vertex appears twice, snip out the part in between the two appearances. Context Let \$u\$ and \$v\$ be vertices of graph \$G\$. If there is a cycle fr...

I think a cycle is not allowed to have repeating vertices, which makes this question trivial

i think you mean a loop

And, request for a test program

lyxal

55 mins ago, by lyxal

I'm just going off what they said at the lyxture :p

55 mins ago, by lyxal

Number Basher

Hmm, ok then

I really think you should remove the edges for simplicity and elegancy and understandability

because it doesn't matter

lyxal

2:23 PM

I did

the challenge already states that edges don't matter in this case

Number Basher

I mean, in the example, the question body

> ... any cycle 𝑣1,𝑒1,𝑣2,𝑒2,...,𝑒𝑚,𝑣𝑚 with a vertex ...

A cycle ... do not travel to any vertex twice. from MSE, math.stackexchange.com/questions/1490053/…

but it also seems that,

> A loop is commonly defined as an edge ... with both ends as the same vertex.

Oh wait, it's called a circuit

> A cycle in graph theory is a closed path i.e., we start and end at the same vertex. In between, **we don't get any chance to travel twice**.

The circuit is defined as a closed trail. It means that it is a path that starts and ends at the same vertex. (so we can travel twice)

from vedantu.com/maths/graph-theory

https://www.vedantu.com/maths/graph-theory

7 mins ago, by Number Basher

And, request for a test program

@lyxal

lyxal

maybe tomorrow

12:28am is way too early/late to be thinking big brain stuff :p

Number Basher

ok, see you tmr

I can post a test program in the comments

Questions for @lyxal : 1. can we output [1,2,7] as [2,7,1]? 2. can we output [1,2,7] as [7,2,1]? 3. [1,2,4,3,2,4,5,3] ==> [1,2,4,5,3] or [1,2,4,3] ? or both OK?

thejonymyster

2:48 PM

i think it has to be 1,2,4,5,3, since the edge between 4 and 5 isn't part of a removable cycle

@thejonymyster @NumberBasher here's where I asked the same thing, and the following discussion where we tried to sort out an explanation because I wasn't understanding it either

in case that helps :-)

Adam

4:05 PM

I have a Python question: why does print(b'\xff') print \xff, but print(*b'\xff') prints 255?

I guess the answer is just "that's how the spec is defined"

DLosc

4:20 PM

@Adam I imagine it's because a bytes object is conceptually an array of bytes. If you print the whole thing, it'll treat it somewhat like a string, but if you index into it (which you're essentially doing by splatting it), you get an integer between 0 and 255.

pxeger

More specifically, print calls str() on its arguments, so print(b'\xff') outputs the __str__ representation of the byte string, which returns an escaped version of it

But when you use print(*b'\xff'), you're splatting the bytestring into the arguments of print. A byte string, when iterated over, returns a sequence of integers for the codepoints

so in this case it's equivalent to print(255, )

and print(*b'hello') is equivalent to print(104, 101, 108, 108, 111, )

Adam

@pxeger I guess my question was "why does iterating over a byte string turn it into an array of integers?"

And the answer to that is "because that's how it's defined"

pxeger

Honestly no idea

Zion mycelia adamancy

@Adam Because a byte string is an array of integers

Adam

I would guess it's because there's no "byte" object

pxeger

4:24 PM

But a string is also fundamentally an array of integers, and when you iterate that you get a sequence of length-one strings

Adam

True, but technically everything is an array of integers on disk

pxeger

I guess it's on the assumption that with bytes you care more about the byte codepoint values

DLosc

If you're iterating over a string of characters, you get each character. If you're iterating over a string of bytes, you get each byte. It's possible that a given byte is only part of a character, so it doesn't make too much sense to treat it as a character.

pxeger

The question is more why don't you get a length-one byte string?

(which, actually, you do in Python 2)

DLosc

Hmm. I had been assuming that a bytes combined multiple bytes into a single character when displayed, but now I see that's not the case. So I guess I don't know. Maybe it's expected that you'll be doing some math on the byte values??

pxeger

4:32 PM

Bitwise operations, more likely

@DLosc bytes has no assumptions about encoding; there's nothing to say it's UTF-8

DLosc

Ah, fair

user

5:11 PM

I just found a site where it says "Longer is better" next to the password field when signing up, and "better" links to xkcd.com/936

Radvylf Programs

5:22 PM

With modern tools I think they're about equally difficult, at least within a few orders of magnitude, since guessing words is another method that people use

Wait no, Munroe took that into account

thejonymyster

still not on a first name basis with randyrands i take it?

also, where does he take it into account? :-) i didnt finded it when i looked at the page

every now and then i consider having a freakishly long uncrackable password but then i worry about 1. forgetting it 2. it being leaked through no fault of my own anyway e_e

well, less forgetting it and more having to type it :P

Radvylf Programs

@thejonymyster Oh no, we go way back.

Met in kindergarten.

(I forgot which was his last name :p)

@thejonymyster 44 bits is 4*11 bits, and 11 bits is a (low) estimate of how much entropy a common english word has, definitely no where near the entropy of all the characters in the word combined

thejonymyster

Mandall Ruht-roh

ahh fair

its always weird when people call him "the xkcd guy"

wait im veering into offtopic, ill ask my associated question in ottnb

user

5:45 PM

@thejonymyster This is why my password is hunter2. Very easy to remember

It's pretty unlikely someone will hack me/Google and take all my monies, right?

thejonymyster

5:56 PM

@user hey, we're password buddies

Steffan

Ooh gimme ur email

Then I can hack all your accounts

user

6:32 PM

@Steffan It's spamspamspam@pxeger.com (yes, really)

thejonymyster

thats a good email

pxeger

7:10 PM

@user whyyyy

thejonymyster

8:28 PM

what if a challenge is too big for a cmc but too small for main

Steffan

CMegaC

pxeger

"CMegaC" is normally for things that are essentially impossible

Steffan

I know

I guess it could just be CC (chat challenge) if it's not mini or mega :P

Unrelated String

8:45 PM

it's categorically a cmc if it's too small for main :P

pxeger

so does chat imply mini?

Unrelated String

or mega

unsuitable for main

pxeger

mini implies chat?

are these labels necessary or sufficient?

someone write a proof

Unrelated String

probably™️

pxeger

Oh guys do you know Unrelated's theorem, one of the most famous proofs in 21st century mathematics? Yeah it was that one that concluded with "yeah, maybe, I guess"

10

Number Basher

10:01 PM

@thejonymyster it can either be [1,2,4,3,...,5,3] or [1,2,4,3,...]

Ohh, anyone? https://2022.galacticpuzzlehunt.com/puzzles

Wait, argh, the server broke

Zion mycelia adamancy

@pxeger "And so, we conclude that the Riemann hypothesis is correct. Maybe. Yeah, maybe. I guess?"

Radvylf Programs

"Yeah I mean this collatz thing looks pretty sound to me. Maybe. Yeah. Yeah."

Zion mycelia adamancy

"Pretty sure P is, like, maybe somewhat in the vicinity of NP, kinda? Like, if we squint, they look like the same roughly similar thing?"

Ginger

"We're about 90% sure that Fermat's Last Theorem is true. Maybe."

Radvylf Programs

10:16 PM

That one's been proved though

And it doesn't end with any probablies :p

Zion mycelia adamancy

@RadvylfPrograms Kinda maybe proved. Why not? Let's say, sure it's been proved

Ginger

has it really though?

Radvylf Programs

Y'know it would be really funny to make a multiple-hundred-page proof of something like P=NP and hide a sneaky little "assuming P=NP" in there somewhere just to waste people's time

On like page 98

Ginger

lmao

Zion mycelia adamancy

@Ginger What if someone finds x, y, z, n such that the theorem is shown to be false? Check mate liberals

Ginger

10:19 PM

dammit :b

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