Mathematics - 2023-07-26 (page 1 of 2)

Ted Shifrin

00:19

And the commentary that ensued …

MathCrackExchange

If anyone would like to join our Theories, Sites, Toposes study group on SE Teams (private) just ping me or drop an email (enjoys math [one word @ the mother google mail]). Screenshot coming up...

It's a neat feature of MSE that I never explored before.

Teams I mean

Requirements: that you purchase Olivia Caramello's book (no pirate copies permitted or promoted)

We'll have rules too, one rule is you don't have to make an attempt in your first post, as we know that you're studying and trying to figure out how to make that first attempt

LaTeX doesn't work OOTB, but luckily you can use either StartChatJax bookmark button or TeX All Things chrome plugin (which also works in SlimJet)

No memes allowed; Unicode emojis welcome

😁🤣👍✌👀😉😎

You could though make your avatar a Meme, etc. That's up to you

I'm beaming out 🌌

MathCrackExchange

00:54

Xander Henderson

The plural of "topos" is "topoi".

X(

Jakobian

01:21

not anymore

MathCrackExchange

01:34

It's either or, the advantage of toposes is you don't need to explain latin suffixes

To the pupil

Any apt pupils in here interested in the theory that bridges all theories?

Maybe not all, but some

Topose theory version 10 might do "all"

up to analytical rearrangment of expressions

We're still at version 0 I believe

Informally speaking

It's important because computerized math understanding requires it. We won't have general AI smarter than us until it can do such math

If you're looking for a math-hating AI, then that would be much easier

If they Hate Algebra though, they're a Heyting Algebra - lol pun

Dang, why does my brain only turn on in the late afternoon, now I got to stay up again to get some work done

My circ. rhythm is probably way off at the moment

Worked 18 hours a couple Sundays ago

@XanderHenderson what is the latest news on the strike?

Am I a scab for using MSE during the strike ... :|

Elon Musk maybe will by SO for 10 billion and make the corporate people listen to its moderators

Random thought

Xander Henderson

491

Q: Moderation Strike update: Data dumps, choosing representatives, GPT data, and where we’re holding

Introduction Since our strike announcement, a number of new developments have occurred. Philippe, VP of Community, posted data they have regarding GPT content on the platform. Stack Exchange staff reached out to strike organizers and asked us to choose three moderator representatives for the str...

MathCrackExchange

Thx, gonna really read it now

Xander Henderson

@MathCrackExchange Disagree. "toposes" is stupid. It is not comfortable in the mouth of an English speaker, and looks dumb on the page.

MathCrackExchange

It's up to the author.

Xander Henderson

Also, "data" is plural (the singular is "datum"). And the plural of "index" is "indices".

MathCrackExchange

01:48

In this case, the author of this book is a genius who probably speaks Latin

I use, datum and indices in code

but usually just data

even if it's a single of something

Xander Henderson

@MathCrackExchange You should be locked up.

MathCrackExchange

That's why mah code is sooo buggy

Nah, everyone's code is buggy who doesn't use formal verification

I want to hopefully get into that side of CS one day. It's amaze balls

shintuku

today i discovered, although chatgpt sucks at mathematics it's great at programming. i just automated like half the programming i needed for something

MathCrackExchange

LOL

@shintuku

It can do somethings, but you're better off just using it as a code completion

Like advanced Vis Studio intellisense

shintuku

yeah i needed some batch stuff and i knew jackshit about it, but chatgpt did all the basics there lol

MathCrackExchange

01:52

Nice. I've never used it. Don't even know what it looks like on the screen

I'm ancient (37) but in my prime

number

shintuku

and i was rusty on a couple of python things, ended up getting it done with chatgpt and got working code

Xander Henderson

@MathCrackExchange 37 is "ancient", now?

Get offa mah lawn.

MathCrackExchange

Next year's going to be get into shape year, and for the next 3 years, because 41, I'll be in my prime again 😂😂

Jakobian

57 is prime

MathCrackExchange

I'm sensing shintuku is about 24?

Only if you're Grothendieck @Jakobian

19 * 3

I once thought 87 was prime, I was like damn I found the pattern

Luckily ChatGPT is there to sus out this primality mess

There is a pattern, but ChatGPT needs to be run on an NSA supercomputer to solve it

j/k

Jakobian

01:58

so far Galois theory is going pretty easy. I probably wouldn't come up with all those things but it's easy to understand

MathCrackExchange

Don't joke

I tried studying the basics about 5x already, still haven't cracked it

You're smart

I mean if that's all I had to do, it would take me maybe 3 months to make it through Lang's chapter on it

Remember Galois theory gets really deep too. It's a good thing to have under your belt

FLT paper uses it only a million times (Galois Rep. Theory)

and Cohomology

I sometimes wonder where all the math comes from. Because Galois only took us to the foundation. Then you see 100's of theorems about it in a textbook, not even cited, and you're like damn how did they...

Which is why a proof database would be a great thing to have access to

one potato two potato

I forgot almost all finite galois theory. I once wanted to learn about galois descent but didn't.

MathCrackExchange

Infinity is where it's at

:D

Jakobian

02:18

at least it has topology in it

one potato two potato

anybody can define any topology anywhere

Jakobian

drinking is not good for you

copper.hat

03:15

all that is not good for you is good for you

Lucky Chouhan

05:10

I have one question see, $$\mathrm{P}_1 = \cos{t} + i \sin{t}$$ And $$ \mathrm{P}_2 = \sin{t} + i \cos{t} $$ We can see that $$\mathrm{P}_2 = \cos\left(\frac{\pi}{2}-t \right) + i \sin\left(\frac{\pi}{2}-t \right)$$ And both are parametrization of circle so what is difference between them?

leslie townes

well, at most values of t, the points P_1(t) and P_2(t) are in different places. that's either one difference, or infinitely many differences. depending on how you count em.

they also travel the unit circle in opposite directions.

they both travel at the same speed. that is a point of non-difference between them.

123

06:37

Hello Everyone..

nickbros123

06:48

what is the level of hubbard hubbard multivariable calc? what to expect,; i have knowledge of real analysis at the sherbert n bartle level, not much linear algebra, 1st 2 chapters of kenneth hoffman and kunze.

one potato two potato

interesting. Hubbard also wrote a book about multivariable calculus?!

it seems the philosophy of the book is the same as ted's multivariable calculus book

nickbros123

@onepotatotwopotato i meant his textbook named linear algebra vector calc differential forms, a unified approach

one potato two potato

07:08

I don't know the level but it's readable under your knowledge (I guess).

John Bull

08:03

Good morning.. How is everyone this fine day?

Number theorists abound?

Thomas Finley

08:51

0

Q: If $D$ is an integeral domain and $D$ is of finite characteristic, prove that the characteristic of $D$ is a prime number.

If $D$ is an integeral domain and $D$ is of finite characteristic, prove that the characteristic of $D$ is a prime number. I tried to solve this as: We know that, The characteristic of an integral domain of a finite characteristic, $D$ is the least of all $p$ such that $\underbrace{a+a+...+a}_{\...

ring-theory proof-writing

Is the proof alright?

Strange that no answers yet!

So, I wondered whether the solution was correct or incorrect?

Oh, guess what? I just got my answer. Someone made a good little comment

user 726941

+1 👍

Vitalie Ghelbert

09:23

Proposition:
Zero parity is neutral.

Demonstration:
a ± 0 = a

🌱

Proposition:
Number one is prime.

Demonstration:
Prime numbers has prime property.
Prime property is inherited number one property of indivisibility.
Number one is prime.
Prime meaning is first.
All primes are named because of that.

🌹

Vitalie Ghelbert

09:44

Rigorous Science was born by Religion over multiple debates.

— Can Science explain what is God and how wide is Zero?
— God meaning is Zero and Zero is infinitely wide as wide as the Universe is
and Zero is Interstellar Space that is the foundation of the Universe and keeps all the Celestial Bodies.

— Is Zero parity odd or even?
— Zero parity is neutral. Let's verity that.
Zero value is neutral, therefore zero parity is also neutral,
that is because value and parity is not changed in relation: a ± 0 = a.

sunny

In the definition of the limit of a function, it is crucial we have $0<|x-a|<\delta$ instead of $|x-a|<\delta$, right?

Because the function may not be defined at $x=a$ when considering a plain limit. Therefor I'm confused about this answer.

Jakobian

10:31

@VitalieGhelbert I hope you're not being serious

Vitalie Ghelbert

@Jakobian I am :)

Jakobian

scary

Vitalie Ghelbert

@Jakobian If needed I can answer questions regarding, to prove my position. Please, I am ready. @};-

Jakobian

I'm doing something right now so I'll pass

Vitalie Ghelbert

@Jakobian O'key then. Good luck and success in what You doing. 🌱

Jaakko Seppälä

10:49

I read from the Internet that Riemann–Roch theorem relates to the case of non-singular algebraic curves. But when I read the book Field Arithmetic, there were no algebraic curves, just an algebraic function field. So how are algebraic curves and algebraic function fields related to each others?

Vitalie Ghelbert

Internet is always wrong.
Internet is not a source of inspiration.
Internet is like a trash.
Never trust a source from the internet.

There is so long we have Internet,
we have so many good books in libraries,
and till our days, we still do not have free access to informational resources from libraries!

More than that, we trying to explore Cosmos, but the whole and entire internet considering "0 is even". :D

Never trust anything, even me.
Always verify!
No ways to verify, therefore it is more probably to be false or wrong!

Jakobian

@XanderHenderson

Sine of the Time

11:05

@VitalieGhelbert what's the matter with you?

Vitalie Ghelbert

@SineoftheTime I am upset on the internet.

Jakobian

@SineoftheTime no need to argue

Vitalie Ghelbert

@SineoftheTime The internet is a garbage dump.

Sine of the Time

@VitalieGhelbert so is this message

Vitalie Ghelbert

On the entire internet I can not find just one people considering "zero parity is neutral" and found nothing about that.
They all considering "0 is even". :D

1 nose, 1 odd, but if no nose, 0 noses is even! :D

Internet is a garbage dump!

Jakobian

11:13

parity is based on divisibility by 2

Vitalie Ghelbert

@Jakobian Yes. And we will always agree for |n| > 0, but when n = 0, "zero parity is neutral": a ± 0 = a.

Jakobian

I'm starting to think you're a troll

Vitalie Ghelbert

@Jakobian What is troll?

@Jakobian troll, trolleybus? 🚎

Jakobian

yeah actually you must be a troll

Vitalie Ghelbert

@Jakobian I am not troll. What is troll, please?

Jaakko Seppälä

11:19

In internet culture, a "troll" refers to a person who intentionally and provocatively engages in disruptive or offensive behavior online.

Jakobian

@JaakkoSeppälä they're acting confused on purpose for someone to engage with them. Just ignore it

Vitalie Ghelbert

Troll (slang)

In slang, a troll is a person who posts or makes inflammatory, insincere, digressive, extraneous, or off-topic messages online (such as in social media, a newsgroup, a forum, a chat room, an online video game) or in real life, with the intent of provoking others into displaying emotional responses, or manipulating others' perception, thus acting as a bully or a provocateur. The behavior is typically for the troll's amusement, or to achieve a specific result such as disrupting a rival's online activities or purposefully causing confusion or harm to other people.In this context, both the noun and...

one potato two potato

A friendly reminder that one can ignore messages from a certain user by simply clicking 'ignore this user (everywhere)'.

Vitalie Ghelbert

No. I am not troll. I am just sad that Internet is not a good source of trust.

Jaakko Seppälä

I know that Internet is not a good source. I just wanted to know how are the two forms of Riemaan–Roch theorem related to each other.

Vitalie Ghelbert

11:27

To be sincere, I was thinking that the duty of Mathematicians is to prevent spreading of such information as "0 is even" on the whole Internet.
Or maybe they also thinking "0 is even"?

@JaakkoSeppälä Maybe they say the same but in different manner?

Maybe this can be of help?
I do not know much about that, but if no body answer to You.
https://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Talovikova.pdf
https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem

Lucky Chouhan

11:44

@leslietownes Thank you for answering! "they also travel tge unit circle in opposite direction" yeah! that's why counter integration of P_1 is 2ipi and P_2's -2ipi.

Peter

@SineoftheTime Can you delete-vote the almost reopened question in CURED ?

sunny

In the definition of a limit of a function, what would be problematic about having $|x-a|<\delta$ versus $0<|x-a|<\delta$?

Jakobian

@sunny that the value $f(a)$ isn't defined for example

sunny

ok, what I thought, thanks!

Jakobian

another thing is that existence of a limit at $x = a$ would imply continuity at that point

but we want to have functions like e.g. $f(x) = 0$ for $x\neq 0$ and $f(0) = 1$ for which $\lim_{x\to 0} f(x) = 0$, yet $f$ is discontinuous

Peter

11:55

@VitalieGhelbert Of course , $0$ is even : An integer $a$ is even , if it can be written as $2b$ with an integer $b$. $a=b$ is not ruled out , so $0=2\cdot 0$ shows that $0$ is even.

Vitalie Ghelbert

Dear and lovely friend, Peter.
What You say, result in simple relation as follows:

0/2 = 0
0 = 2 * 0
0 = 0 + 0
0 = 0 + 0 + 0

0 + 0 = 0 + 0 + 0
Therefore, 2 * 0 = 3 * 0

Let's see when we have |n| > 0.
2 = 1 + 1
3 = 1 + 1 + 1
2 * 1 ≠ 3 * 1

Therefore, 2 * 0 = 3 * 0 is not unique to result and prove "0 is even".
True? :)

Jakobian

If you have a definition you got to stick to it. Manipulating expressions shows nothing

Vitalie Ghelbert

a ± 0 = a

if a is even:
2 * n + 0 = 2 * n

if a is odd
(2 * n + 1) + 0 = (2 * n + 1)

Therefore, 0 neutral value does not change value of number "a",
resulting 0 parity is also neutral.

@};-

Peter

Weird argumentation ! $3\cdot 0=0$ does not make $2\cdot 0=0$ wrong , it only tells us that $0$ is also divisible by $3$.

Vitalie Ghelbert

Look, we can formulate as a Problem of Logic.

Argument A is the reason that statement S is true, otherwise S is false.
If exist argument B equivalent A, A become non-reason argument, therefore neither A or B imply S is true, therefore S is false.

Will result S is true or false, if:
A is "0/2 = 0"
B is "0/3 = 0"
S is "0 is even".

Demonstration that B is equivalent B:
0/2 = 0
0 = 2 * 0
0 = 0 + 0
0 = 0 + 0 + 0
0 = 3 * 0
0/3 = 0
Resulting B is equivalent A.

Will be S true or false?

@};-

Hups! Some errata.

Demonstration that B is equivalent A:
0/2 = 0
0 = 2 * 0
0 = 0 + 0
0 = 0 + 0 + 0
0 = 3 * 0
0/3 = 0
Resulting B is equivalent A.

Jakobian

12:08

there's nothing else to say than your logic is wrong
and the reason it's wrong is something you should be able to understand yourself by self-examination

self-examination is something that requires carefully looking at your own argument

Vitalie Ghelbert

@Jakobian We cannot say "0 is even", because we can 0 = 0 + 0, absurd!

Peter

I gave the definition of when an integer is even. And the condition is satisfied for $0$. End of the story.

Soumik Mukherjee

This reminds me of the quote, "Those who believe without reason cannot be convinced by reason"- James Randi

2

Vitalie Ghelbert

O'key, You want to say that 0 boys and 0 girls can make 0 couples and get married? :D
Because 0 is even? :D
Absurd!

Jakobian

mathematics is a bit like religion
we have our dogma (ZFC) that we stick to, but we don't break the rules of ZFC at any circumstance. If you defined what even means, and you've shown that $0$ is even, then $0$ is even. You can try to disprove it, but it requires an actual argument, that you never provided

that's probably the last thing I'll say in this discussion. Please avoid spamming or I'll have to flag you

Vitalie Ghelbert

12:15

If 7 billions of people of the planet Earth believe that "0 is even", that does not means that became to be truth.
Truth does not matter how many people believe what.

Peter

ZFC has not deserved to be compared with religion.

s.harp

Watching this discussion is like the old days when engineers would fight about 0.999.... = 1

Peter

I am out as well. This discussion begins to hurt.

Vitalie Ghelbert

@s.harp Yes, good point, because 9 * 1/9 ≢(1/9) * 9

Peter

Another nonsensical claim ! The multiplication of rationals is commutative. I am really out now.

Vitalie Ghelbert

12:19

Yes, rigorous science was born by religion over many disputes!

Jakobian

@Peter I think it's accurate though. We just made our beliefs rigorous.

Vitalie Ghelbert

0/2 = 0 => 0 = 2 * 0 => 0 = 0 + 0 and this demonstrate "0 is even"? ABSURD!
Because 0 = 0 + 0 + 0 => 0 + 0 = 0 + 0 + 0. What is the difference?

Jakobian

the only difference is that it's frowned upon for someone to use a different axiom system without mention (unless it's ZF I suppose)

Vitalie Ghelbert

Ooo! Yes, I know. We may say therefore "0 is even", because "Paris is the capital of France".

What are these ZFC and ZF acronyms, please, if You do not mind. I do not know them yet.

Jakobian

ZF means Zermelo-Frankel set theory

ZFC means ZF with axiom of choice

Vitalie Ghelbert

12:25

@Jakobian Thank You, but to complex for me.

Vitalie Ghelbert

12:37

me@amadeus:~$ bc -q
scale = 66
1/9
.111111111111111111111111111111111111111111111111111111111111111111
9 * 1/9
1.000000000000000000000000000000000000000000000000000000000000000000
(1/9) * 9
.999999999999999999999999999999999999999999999999999999999999999999
me@amadeus:~$

Our programs reflect what we are thinking!

me@amadeus:~$ octave -q
octave:1> mod(10,0)
ans = 10
octave:2> mod(0,0)
ans = 0
octave:3>
me@amadeus:~$ python3 -q
>>> 10 % 0
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: integer division or modulo by zero
>>> 0 % 0
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: integer division or modulo by zero
>>>
me@amadeus:~$ # a/b = (q, r) => b * q + r = a.

Xander Henderson

@Jakobian What?

Vitalie Ghelbert

@XanderHenderson, good morning, even if it is evening.
I saw You posted something related to Squaring the Circle information.
Let me please to share some example too.

Xander Henderson

12:53

@VitalieGhelbert No, thank you. I am not interested.

Vitalie Ghelbert

@XanderHenderson You are welcome any way. 🌱

import math

p = 6
n = 10 ** p

sum_h = 0
for i in range(n+1):
h = (i * (n - i)) ** (1/2)
sum_h = sum_h + h

pi0 = 8 * sum_h / n / n

print(" ", math.pi)
print("~", pi0)

3.141592653589793
~ 3.141592650263593

Hm, chat does not support latex.
Chat does not support code samples.
So annoying!

🍎

Proposition:
Number one is prime.

🍏

Algorithms of root and power at any real number order from any real number base.

Jakobian

13:14

@XanderHenderson I just thought you could handle this as a moderator

with your moderator wisdom

Xander Henderson

@Jakobian I'm on strike.

I also don't see anything that would, under ordinary circumstances, be moderatable.

s.harp

I'm guessing that spamming pages of nonsense into the void will result in a mute at some point

Jakobian

@XanderHenderson It was causing me great distress

one potato two potato

13:37

in my experience, the usual situation that moderators intervene is when someone insults another (it could be itself) by swearing in chat.

sunny

Consider the definition of the limit of a function: Let $f:A\to\mathbb{R}$, where $A\subseteq \mathbb{R}$, and suppose that $c\in\mathbb{R}$ is an accumulation point of $A$. Then $$\lim_{x\to c}f(x)=L$$ if for every $\epsilon>0$ there exists a $\delta>0$ such that $$0<|x-c|<\delta \text{ and } x\in A \text{ implies that } |f(x)-L|<\epsilon.$$

My lecture notes claim the following:

> The limit definition would be vacuous if it was applied to a non-accumulation point, and in that case every $L\in\mathbb{R}$ would be a limit.

I don't understand that sentence. Why would it be vacuous and why would every $L\in\mathbb{R}$ be a limit? Maybe an example would help here.

one potato two potato

I always confuse the right coset notation. what is quotient by what.

Xander Henderson

13:53

@Jakobian You have the ability to mute users. If the room owners find it problematic, they can act. There is nothing here (so far as I can see) which requires moderator intervention.

And if it does, feel free to flag.

Peter

@Jakobian The reason for this strike is that apparently noone can control anymore the distrtibution of AI-generated posts. Nice world we live in :( I was always an enemy of artificial intelligence. I prefer the natural intelligence.

Xander Henderson

@Peter One of the more significant motivations for the strike is SE's policy which forbids moderators from moderating content simply for being GenAI, unless the person who posts it admits to posting AI generated text.

More generally, it is about the lack of communication from SE, particularly when it comes to moderator policies (which are supposed to be discussed with the moderators before they go into effect), and the discontinuation of data dumps.

493

Q: Moderation Strike update: Data dumps, choosing representatives, GPT data, and where we’re holding

Introduction Since our strike announcement, a number of new developments have occurred. Philippe, VP of Community, posted data they have regarding GPT content on the platform. Stack Exchange staff reached out to strike organizers and asked us to choose three moderator representatives for the str...

discussion moderation community company moderation-strike

Jakobian

I think AI policy should be adjusted to the stack community

for mathematics it should be moderated I think, for example

but might be okay to use it for other stack exchanges (?)

Xander Henderson

@Jakobian Prior to SE tell us that we couldn't moderate GPT content simply for being GPT content, that was the way it worked. Every SE sub-site had its own policy.

Vitalie Ghelbert

The answer is simple: if You do not want to be disturbed, make a closed community and bring users strictly by invitations only.
Do not let doors open for anyone.

sunny

14:00

@sunny what counts as a "non-accumulation point", anyway? Are those simply the isolated points?

porridgemathematics

@sunny for a non accumulation point $c$, in tiny neighbourhoods of $c$, other than $c$ itself, there are no points of $A$

Xander Henderson

@VitalieGhelbert (1) The problem is not that we don't "want to be disturbed" (whatever that means) and (2) making a closed site rather fails to achieve the stated goal of SE, which is to have an open, accessible, user generated, user moderated collection of knowledge, in the form of questions and answers.

porridgemathematics

@sunny which means the statement 'if $0 < |x - c| < \delta$ then $|f(x) - L| < \epsilon$ will always be true for all $\delta > 0$ sufficiently small, and every $\epsilon > 0$ and every $L$

because the hypothesis, that there are any $x \in A$ , $0 < |x-c| < \delta$ is always false anyway

one potato two potato

It's scary that as time flies, one has to move on from well-organized books to messy and unordered papers.

porridgemathematics

so $|f(x) - L| < \epsilon$ holds for any $L$ at all and any $\epsilon $ at all, heck, even negative $\epsilon$, simply because there are zero candidates for $x \in A$ that aren't equal to $c$ and are within a $\delta > 0$ radius of $c$ when $c$ is a non-accumulation point to test the statement with

Vitalie Ghelbert

14:04

@XanderHenderson Yes, i know, You are right, but I already lost count of how many questions on MathStack were closed or deleted, that means I am not welcome, therefore, why not to make MathStack a closed community open just for those who are welcome?

Xander Henderson

@onepotatotwopotato I mean, that is what happens as you go from well-established and well-understood knowledge out towards the cutting edge of what is known.

porridgemathematics

@onepotatotwopotato tell me about it. also messy and unorganized very recently published manuscripts based on papers virtually noone but 10 people know about

Xander Henderson

Try to read Newton or Leibniz for a view of what calculus looked like when it was cutting edge.

porridgemathematics

even if those manuscripts are now textbooks, they can still be (and often are) messy and unorganized

sometimes just (as written )wrong..

sunny

@porridgemathematics I see, thanks for the response! So I take it a non-accumulation point is just an isolated point, i.e. a point where there is some tiny neighborhood around that point that does not contain any point in $A$.

porridgemathematics

14:08

@XanderHenderson thats true, but there is usually a huge difference in polish of presentation between even stuff that is now "old" (say within a decade or two old) in fields that aren't held under wide scrutiny, and hot fields

a lot of academic writing is so needlessly garbled

@sunny yeah

Xander Henderson

@porridgemathematics Note that I didn't say "old". I said "well-established and well-understood".

porridgemathematics

ah okay, thats fair enough

i guess it also makes me feel slightly better about unfurling stuff that may not be completely new but is definitely not widely known and understood

but i do get why this happens, pretty much every time I unfurl something that is ultimately straightforward, but requires work, i dont bother writing down the laborious details

i just move on when it clicks

Vitalie Ghelbert

14:42

When I read the whole and entire Internet saying "0 is even",
I have impression there is no any more mathematicians in the world!

I am very upset at the Internet,
that seems more to be a garbage dump,
than of source of trust.

🌳

Xander Henderson

What is the definition of "even"?

porridgemathematics

@VitalieGhelbert the internet is a bastion of trust. Every single thing you read on the internet is true. Including this.

Vitalie Ghelbert

@XanderHenderson Classical definition n/2 = k, for |n| > 0, but for n = 0, "zero parity is neutral": a ± 0 = a.

Xander Henderson

@VitalieGhelbert That is not the classical definition.

Which means that you have a different definition from everyone else in mathematics.

That's fine.

Vitalie Ghelbert

No. Internet is not the place of trust. Internet is garbage dump.
Internet is 🌹 dangerous place.

Xander Henderson

14:47

You are going to get different results from everyone else.

And you are going to have difficulty communicating with everyone else.

But it is arrogant to say that you are right, and everyone else is wrong.

porridgemathematics

im amazed this person is still thinking about this lmao

it requires a very special kind of mental fortitude

Vitalie Ghelbert

I know I am right,
because they say "0 is even",
because 0/2 = 0 => 0 = 2 * 0 => 0 = 0 + 0. Absurd!

porridgemathematics

@XanderHenderson he was trying to get chat gpt to back him up on this the other day

Xander Henderson

@VitalieGhelbert Like I said, you are very arrogant.

And you seem not to even understand the definition of even that other people give.

Again, you are welcome to invent the term "neutral element". That's fine. No one else uses it, but if it helps you to prove new results, great!

But what it is not doing is helping you to communicate with others.

Vitalie Ghelbert

Dear and lovely friend, if we say "0 is even",
because "0/2 = 0 or 0 = 2 * 0",
it is the same to say "0 is even", because "Paris is the capital of France".
Absurd! :)

Xander Henderson

14:50

@VitalieGhelbert Which is why no one has made that argument.

Not in isolation, anyway.

First, you define a word.

Once you have a definition, you can then check to see if the objects you are working with fit that definition.

There are a number of more-or-less equivalent definitions of "even" commonly used in mathematics. The number 0 meets all of those definitions.

Whether or not you believe it to be "absurd".

Vitalie Ghelbert

Dear and lovely friend,
I can also define this question in a Problem of Logic:

Argument A is the reason that imply statement S is true, otherwise S is false.
If exist argument B equivalent with A, A become non-reason argument,
therefore neither of A or B will imply S is true, therefore S is false.

If we define:
A is "0/2 = 0"
B is "0/3 = 0"
S is "0 is even"

B is equivalent A:
0/2 = 0 =>
0 = 2 * 0 =>
0 = 0 + 0 =>
0 = 0 + 0 + 0 =>
0 = 3 * 0 =>
0/3 = 0 => B is equivalent A.

Resulting statement S is true or false?

Xander Henderson

This is nonsense.

Jakobian

@XanderHenderson what are those definitions

I only know of one

Vitalie Ghelbert

@XanderHenderson Yes, it is nonsense, because we can say "0 is even", because 0 = 3 * 0, because 0 * 2 = 0 * 3. Absurd!

Xander Henderson

@Jakobian 1. An integer $n$ is even if there exists an integer $k$ such that $n=2k$.

2. An integer $n$ is even if, when divided by $2$, the remainder is $0$.

Vitalie Ghelbert

14:57

@XanderHenderson Exact, for |n| > 0, works just fine, but not for n = 0.

Xander Henderson

3. An integer is even if it is in the set $2\mathbb{Z}$.

@VitalieGhelbert It works perfectly well for any integer, including negative integers.

Jakobian

I don't know, they all sound the same to me

I thought you had something peculiar in mind

Xander Henderson

@VitalieGhelbert (1) I don't see how this is absurd. (2) I don't see how this shows that 0 is not even.

Check the definition.

@Jakobian Yes, they are more-or-less equivalent.

Vitalie Ghelbert

@XanderHenderson Exact, every number that can be represented as sum of 1 (units), but not for n = 0.

Xander Henderson

Depending on what machinery you want to use.

@VitalieGhelbert The definition of "even" makes no reference to "units".

Thorgott

15:00

an integer $n$ is even if $n=0$ or the integer $n-sgn(n)$ is odd

Xander Henderson

@Jakobian The point is that if you want to talk about remainders, you have to first know that remainders exist, so you need to first prove the division algorithm.

For example.

The definitions are all essentially the same, but built from different foundations.

Vitalie Ghelbert

It does. Look.
2 = 1 + 1
3 = 1 + 1 + 1
1 + 1 ≠ 1 + 1 + 1
See?

But what we have for 0 case:
0 = 0 + 0
0 = 0 + 0 + 0
0 + 0 = 0 + 0 + 0
Therefore, n/2 = k, works just for |n| > 0, not for n = 0.

Proposition:
Zero parity is neutral.

Demonstration:
a ± 0 = a.

0 value is neutral and does not change value of the number "a",
therefore 0 parity is neutral also.

@}:-

Xander Henderson

@VitalieGhelbert You are just repeating the same nonsense you have repeated before.

Jakobian

You're repeating the same thing over and over without much thought

Xander Henderson

It didn't make sense then, and it doesn't make sense now.

Jakobian

15:03

it's no different than talking to a wall

Vitalie Ghelbert

Yes, but what You say for "0 is even", result in because 0 = 0 + 0?!

Xander Henderson

The set $2\mathbb{Z}= \{\dotsc, -4, -2, 0, 2, 4, \dotsc \}$. If we define even numbers to be elements of $2\mathbb{Z}$, then $0$ is even. I have provided a definition of what it means for a number to be even, and have demonstrated that $0$ fits that definition.

This is how mathematics works.

Jakobian

Yes, $0$ is even because there exists $k$ such that $0 = 2k$. This $k$ can be taken to be $k = 0$

Xander Henderson

We define a term, then investigate the consequences of that definition.

@Jakobian That also works.

Jakobian

This is what it means, $n$ is even if there is $k$ such that $n = 2k$

here $n = 0$

Vitalie Ghelbert

15:06

If we have 1 mosquito between 100 elephants,
1 mosquito will became elephant too?

Same here, with 0 between infinitely many even numbers in pattern n = 2 * k, for k in Z.

Jakobian

please stop non-sensical arguments

Xander Henderson

@VitalieGhelbert I fail to see the relevance of mosquitos and elephants.

s.harp

Eating Baklava often one quickly gets tired of it, but eating it once every so often it is simply divine

Vitalie Ghelbert

If we have 1 elephant between 100 mosquito,
1 elephant will became mosquito too?

Same analogy 0 with neutral parity between infinitely many evens in this patter n = 2 * k, for k in Z.

Xander Henderson

@s.harp I made baklava once, from scratch.

That was quite an ordeal. The result was great, but I ain't doin' it again.

Sine of the Time

15:07

@Peter I don't have enough rep I think

Xander Henderson

@VitalieGhelbert I fail to see the relevance of mosquitos and elephants.

(If you are going to cut-and-paste, so am I.)

s.harp

@XanderHenderson I believe you, I think its an all day kind of ordeal, even for Turkish Grandmas

Vitalie Ghelbert

@XanderHenderson If I understood correctly, I am writing by hands from keyboard. No copy paste.

Xander Henderson

@s.harp I took a day to make the filo, then actually made the baklava the next day.

Jakobian

@VitalieGhelbert rolls eyes that's not the point...

the point is you repeat the same thing with the exact same words, no matter if you copy paste it or type it all

Xander Henderson

15:09

@VitalieGhelbert You are so concerned with being technically correct that you have entirely missed the point.

You are failing to communicate, because no one understands what you are talking about.

Vitalie Ghelbert

O'key.
Let's see examples.

4/2 = 2 remainder 0

You say 0/2 = 0 remainder 0. Right?

Therefore, "0 is even".

If so, 0 boys and 0 girls can make 0 couples, and because 0 is even, they can get married?
Correct or Absurd?

🌳

Xander Henderson

@VitalieGhelbert NO.

I said that even numbers are elements of the set $2\mathbb{Z}$.

Ted Shifrin

I want to put the whole room on time out.

Xander Henderson

That is, $2\mathbb{Z} = \{ 2k : k \in \mathbb{Z}\}$. $0$ is very clearly in that set, therefore, per the definition I have provided, $0$ is even.

This has nothing to do with boys and girls and married couples. Those things are utterly irrelevant.

Vitalie Ghelbert

This pattern n = 2 * k, for k in Z, will be exclusively only even numbers, when:

n = 2 * k, for k in Z{0}.

0 parity is neutral,
that is why a + 0 = a.

Value is not changed as do even numbers in:
2 * n + 2 * m = 2 * (n + m)

but for 0 case:
2 * n + 0 = 2 * n.

Soumik Mukherjee

15:13

I always wished that some human will single handedly compete against chatgpt's monopolization of writing nonsence and calling it mathematics.

Jakobian

> If so, 0 boys and 0 girls can make 0 couples, and because 0 is even, they can get married?

This has nothing to do with parity of $0$, but yes, they can get married, trivially

GratefulDisciple

@s.harp I would love it except that I want a baklava with meat, maybe something like this but with filling similar to Dutch Saucijzenbroodjes. It would be a kind of baklava fusion I would consider divine.

Jakobian

how do I stop it from citing the whole message

Xander Henderson

@VitalieGhelbert You aren't listening to what I am saying, and are not responding to the points that I have made. I am muting you, now.

Vitalie Ghelbert

If we have 10 boys and 10 girls, how many dance couples can we have?

Logically 10 couples: 1 boy with 1 girl.

Jakobian

15:15

@VitalieGhelbert I don't care. Should I?

Xander Henderson

@VitalieGhelbert Before I mute you: this is very heteronormative. Boys can dance with boys, girls can dance with girls, and there's no reason there couldn't be a thruple or two.

Vitalie Ghelbert

Trivial explanation:

3: 🍏🍏🍏
2: 🍏🍏
1: 🍏
0: zero apples, therefore zero parity is neutral: neither odd nor even.

No object, no units, You want to say because: 0 = 0 + 0? Absurd!.

The whole and entire Internet saying "0 is even".
Who is mathematician that must know what is what and when?
Me? I am not mathematician.

Jakobian

> therefore zero parity is neutral: neither odd nor even.

why are you making a conclusion out of thin air?

by the way, you should look up what out of thin air means if you don't know that

Vitalie Ghelbert

Human has 2 arms, 2 legs, 2 eyes, 2 ears. Even.
1 nose, 1 head, 1 is odd.

Jakobian

That's very clear to me

Vitalie Ghelbert

15:22

I cannot be wrong.
What I say may be wrong.
"0 is even", because 0 = 0 + 0, is false.

Jakobian

But if you're not a mathematician then why are you trying to correct them?

I know those kind of issues can be present because of physical conditions e.g. brain tumor. I disagree with everything you say, but I hope you have a good day.

If everyone is telling you that you're wrong, then maybe you really are wrong? Let's stop pretending

Vitalie Ghelbert

Jesus Christ after he died at 3 years old without being born said : "0 is even", because "Paris is the capital of France".

:D

Thorgott

sometimes sticking to the ancient wisdom of "don't feed the trolls" is the right call of action

GratefulDisciple

@XanderHenderson Yeah, problems like this happen occasionally in Christianity.SE. There is a kind of "tradition" in every discipline where important topics and relevant discussions about a topic are using common terms that over time acquire established meanings. There's a kind of expected etiquette where new participants need induct themselves to the discourse by educating themselves with traditional usage of the terms so the community as a whole can be enriched.

Vitalie Ghelbert

God was created by Humans, not Humans were created by God.

Xander Henderson

15:28

@GratefulDisciple Yeah, it is pretty much the foundation on which all of mathematics is built. We agree on a small number of axioms, a deductive system of some sort, and work out from there.

GratefulDisciple

It used to be that liberal education helps one to be "inducted" into the great conversation by requiring them to study the great books.

Xander Henderson

When it is convenient, we condense some ideas by defining new terms which stand in for more complicated things.

And we continue to work out from there.

Let's please not engage in these kinds of speculations.

Vitalie Ghelbert

God is lies and untruth.
Religions are lies and untruth.
Because all of these were created by humans.
Therefore Science is same as Religions and God.

Xander Henderson

@VitalieGhelbert I would very much encourage you to stop. I think that the other participants in this room have made it clear that this kind of interaction is not appreciated.

Let someone else have the floor for a while.

Jakobian

@XanderHenderson sorry

GratefulDisciple

15:32

@XanderHenderson Being active in C.SE I'm tempted (but only very little) to respond to those sentences with religious terms, but I don't want to feed the trolls :-), at least not in a Math chatroom.

Vitalie Ghelbert

— Can Science explain what is God and how wide is Zero?
— God meaning is Zero and Zero is infinitely wide as wide as the universe is,
and Zero is Interstellar space that is the foundation of the universe and keeps all the celestial bodies.

But what we find in the internet about God?
Lies and Untruth!

A lot of interpretations that trying to guess: what could be? :D

Xander Henderson

@GratefulDisciple It is appreciated.

Jakobian

@GratefulDisciple what is C.SE?

GratefulDisciple

@Jakobian Christianity.SE; there is a main chatroom related to it where questions & discussions about religion from the point of view of Christianity are welcomed. StackExchange has SE for each of the other major religions too.

Jakobian

I see. I'm an atheist though

GratefulDisciple

15:37

@Jakobian So does @冥王Hades. We welcome inquirers :-).

Vitalie Ghelbert

I am neither atheist,
I am just:
"i know i do not know,
that is everything i know,
but at least i can to try to figure it up"

🌹 rose dangerous

Jakobian

I was raised in - somewhat neglectfully - Christian family, so I know the basic principles. I'm not interested in religion though

Although I do believe in the good that religion provides for the families with lost relatives

Vitalie Ghelbert

Oh no! I am convinced that You know Coordinate System.
If so, You know everything You need to create the whole and entire universe as "God did".

Example:

Coordinate System axes defined with function => f(x) = 0/x => (x, 0) axis and (0, y) axis.

Jakobian

I believe that religion is good for society at whole

I have my own views on philosophy etc. but I believe them to be good enough, so I don't feel the need to discuss them

Vitalie Ghelbert

Dear and lovely friend, Religion is like a hammer, depending who is keeping hammer from tail.
Religion is an instrument.
Science is an instruemnt.
Hammer is an instrument.

When hammer as instrument is good for?
Same Religion and Science, depending who is keeping in who's hands.

Same Mathematics as Religion.
What will happen if this full of lies and untruth behavior of religion will make Mathematics definitions?

Santa Lucia, Mama Mia! Inquisition!
Same here "0 is even", because 0 = 0 + 0. ABSURD!

Augusto Matteini

15:50

Does anyone know how does he conclude with the implicit map theorem? I don't understand why g has to be equal to f. After that it is clear but I don't understand neither how does he know that it should have g(y)=f(y) neither why the condition implies the equality of the 2 functions thank you.

GratefulDisciple

@Jakobian Yeah.... suffering is often when people turn to religion; questions start when they need to adjust their mental concepts to their lived reality to address the existential concerns that arise. That's when they often find the concepts they thought they knew were not sufficient (either incomplete, unhelpful, or contradictory) which then lead to discussion. Feel free to follow up at The Upper Room.

s.harp

Sending emails who's sole content is "👍" - hip or uncool?

Xander Henderson

@s.harp Yes.

Jakobian

16:11

how do I write $\{$ and $\}$ on github?

Vitalie Ghelbert

Jakobian

16:55

does MR require subscription of some kind?

s.harp

Whats MR

Jakobian

the mathematical reviews number on AMS

I have MR2048350 for Willard topology book, but I can't even search for it on their site

I'm trying to figure out how to obtain a MR from a book

for referencing

Ted Shifrin

Mathematical Reviews is like a journal. People actually write the reviews. In my day, we would go to the library and look it up in huge books. Now it's searchable on-line as MathSciNet. But you need an institutional membership to get to it.

Transcript for

$Mathematics$ Mathematics