Mathematics - 2015-06-28 (page 1 of 3)

Mew

12:36 AM

hello

anyone online?

Mary Star

12:49 AM

Hello @Mew !!

Mew

1:11 AM

Hi Mary

Soham Chowdhury

@MGA Check all the conditions one by one.

Mew

G'day Soham

do you know about the many body problem?

Soham Chowdhury

Nah, don't know much physics (if that's what it is).

Actually, don't know much of anything. :P

robjohn

2:00 AM

@Mew Haven't seen you here in a while...

Fargle

2:43 AM

Strange question, that I haven't found an answer to yet: every group $G$ is isomorphic to a subgroup of the permutation group on the set $G$. Is there a similar, more specific way to classify rings?

Soham Chowdhury

@Fargle I believe I saw some related question on MSE which said no.

Fargle

@SohamChowdhury Hmm. I'll look for it.

Soham Chowdhury

32

Q: Why is there no Cayley's Theorem for rings?

Cayley's theorem makes groups nice: a closed set of bijections is a group and a group is a closed set of bijections- beautiful, natural and understandable canonically as symmetry. It is not so much a technical theorem as a glorious wellspring of intuition- something, at least from my perspective,...

"Wow. You know that thing where everyone seems to know a secret but you? I'm so there right now."

Hahahaha

Fargle

@SohamChowdhury Haha, what a great quote. And this is exactly what I'm looking for, thank you! I'll have to digest this a bit.

"Rings act on abelian groups, groups act on sets." ...whoa.

Soham Chowdhury

3:13 AM

So, what acts on a, uh, corps commutatif, @Fargle?

I figured out the reason why I have so much trouble studying point-set topology, @Fargle, so I'm really happy now. It's not point-set so much as it is nitty-gritty analysis things which I don't like. (Which are pretty much only a single chapter)

Fargle

@SohamChowdhury I would suspect that a field $F$ would necessarily be a subring of the endomorphism ring on $(F, +)$ such that $F^{\times} \subseteq \mathrm{Aut}(F,+)$.

Semiclassical

Hmm. I wonder if the following question has a known answer: Let $m,n$ be nonzero integers. Given a positive integer $a$, under what conditions will there exist integers $b,c$ such that $a=mb^2+nc^2$?

Fargle

@SohamChowdhury Yeah, analysis can be pretty icky. What in particular gave you trouble?

Semiclassical

The case of $m=n=1$ is essentially Fermat's theorem on sums of two squares, and that page also discusses some results of the above kind. But it doesn't give a systematic statement.

...and then i notice the citation at the bottom to a book entitled "Primes of the form $x^2+n y^2$".

Semiclassical

3:32 AM

okay, turns out it's a well-understood question. good to know.

Fargle

@Semiclassical What conditions did you find?

Semiclassical

didn't say i found the answer, just determined that it's a well-known problem :)

Fargle

Oh. Well then.

Semiclassical

it falls under the following rubric: Given a particular quadratic form with integer coefficients, what integers can it represent?

Fargle

That makes a lot of sense. That makes it a pretty "standard" number theory question, it seems.

Semiclassical

3:47 AM

right.

one user on OEIS has a page discussing the case of binary quadratic forms in particular, including links to some example sequences (e.g. positive integers representable as $x^2+y^2$)

Fargle

Huh. I can't wait until some of this stuff doesn't go over my head.

Semiclassical

Encyclopedia of Math also has a page on it: encyclopediaofmath.org/index.php/Binary_quadratic_form

Fargle

I'll have to read that in the morning when I'm not stupid.

Goodnight all

Semiclassical

night

skill patrol

Later pal.

Stan Shunpike

4:40 AM

@TedShifrin I am a bit confused about $LAL^T$ in your lecture on quadratic forms. You say something like suppose I have a matrix $L$ and $U$ and suppose $U$ is similar to $L$ but not quite. I need a matrix that will allow me to "fudge", meaning operate on $U$ in such a way that it becomes like the transpose of $L$. And you give an example of a matrix that does this.

@TedShifrin but is there a name for being "almost like" a transpose? That sounds like a concept that would have a name. Or I may just be missing something....

@TedShifrin by the way, this is a really really really fun example. I had no idea how much fun simple quadratics could be again :P

Sorry! The matrix in the middle is $D$ for diagonal

anon

4:57 AM

@Fargle I don't see the connection between your two sentences. Cayley's theorem is in no way a "classification" of groups...

Soham Chowdhury

I just don't like the stuff that falls into a first chapter -- show that the interior operator is idempotent etc. All that epsilon-delta pushing isn't really to my taste.
And I doubt it actually appears elsewhere until you're studying advanced analysis or "advanced general topology", whatever that might be.

Lembik

5:15 AM

hi

anyone interested in a tricky puzzle?

1

Q: Finding real money on a strange weighing device

You have 50 coins which each weigh either 20 grams or 10 grams. Each is labelled from 0 to 49 so you can tell the coins apart. You have one weighing device as well. At the first turn you can put as many coins as you like on the weighing device and it will tell you exactly how much they weigh. H...

combinatorics puzzle

Stan Shunpike

5:31 AM

@Lembik that's a really fun question! +1

Where did it come from?

Lembik

@StanShunpike It's a variant of a famous puzzle that I made up

and thank you :)

@StanShunpike I think the first challenge is to solve it in 49 weighings :)

Stan Shunpike

Why?

oh sure

You mean one less than 50

@Lembik one interesting thing I noticed was I'd you put one coin in, it could weigh10 or 20. If you put 2 in, 20,30,40...you put 3 in, 30,40,50,60

So the number of possible options is always the number of coins +1

I am not qualified to answer this, but it is fun brainstorming

Lembik

5:47 AM

yes one less than 50.

please brainstorm away :)

Stan Shunpike

6:00 AM

@Lembik for two coins I think it takes 50 trials too.

Have you tried this? What did you get?

Lembik

@StanShunpike I have tried it for small ones.. I get 8 weighings for 12 coins

I am sure you can do it in less than 50 weighings as you always use fewer than n weighings for every case I have tried

but I don't know what the optimal number is

Soham Chowdhury

@AlexClark, what happened to your . . . challenge?

Stan Shunpike

@Lembik The order of the coins makes no difference. So the problem is about for a given measurement, how many possible weights could it represent. Like if you get 30 and you have 3 coins, they all must be 10.

And like you say, all the weighings are predetermined.

So they constitute a set we know apriori once we decide how many coins to put on.

Lembik

yes

@StanShunpike well.. once you decide which coins to put on

that makes a difference

Remember me

6:37 AM

Let $A\subset X$ let $f : A\to Y$ be continuous ,let Y be hausdorff . Show that if f may be extended to a function $g :\bar{A} \to Y$ then g is uniquely determined by f

I want to know what they mean by uniquely determined by f

Soham Chowdhury

It means, given a fixed $f$, there is only one fixed $g$.

Remember me

How should I prove that??

Soham Chowdhury

That's your problem, not mine :P
And use a single question mark.

Remember me

Why?? :p

I always get stuck at the last question

Soham Chowdhury

Because people are nicer to you if you look different from anyone on this sub :P

Remember me

6:42 AM

So the question means that if I expand the domain of the function $f$ then i will always reach only $g$ right @Soham

Soham Chowdhury

Yes.

Remember me

Thats pretty nice

Seems like a nice exercise

Soham Chowdhury

That sub is epic.

Remember me

Counter strike

Soham Chowdhury

@AlexC: link is on point but pretty weird

Huy

7:28 AM

Morning, kids.

How's everyone this fine day?

skill patrol

Fine thanks. How are you pal :-)

Huy

Same, just woke up and I'm starting the day with a cup of coffee and extending my city in Cities Skylines a bit before going on with some more DiffGeo.

Balarka Sen

@SohamChowdhury Well, it totally is an AT obsession (i.e., wanting to learn only one subject without knowing what it's about). But I won't tell you what to do anymore, as it's apparently unwelcome.

All of mathematics is "deep stuff". sigh.

3

Destiny freedom

7:48 AM

if $$(y'(x))^2=2\cos{y(x)},y(0)=\dfrac{\pi}{2}$$ show that $y(x)=y(-x)$

Random Variable

8:03 AM

@Huy I've watched Let's Plays of Cities: Skylines on YouTube. These days I seem to spend more time watching people play computer games on YouTube than actually playing computer games myself.

Huy

8:56 AM

@RandomVariable: You should try it. It's amazing.

@RandomVariable: I think it's the best game I've ever bought.

Random Variable

@Huy Do you need a really good graphics card for it to run smoothly?

Huy

9:10 AM

@RandomVariable: Not sure, check out their website. I got a decent PC so I don't worry about that stuff. (7950 GPU)

@RandomVariable: I think CPU and RAM will become more important as you proceed in the game. Tbh I've never managed to get a population over 50k yet, so I can only guess.

Soham Chowdhury

10:02 AM

@BalarkaSen How am I supposed to know what something is about, as you say, without learning it first? How do I learn something before I learn it?

Isn't it possible that I simply like the questions topology talks about, and want to know about them?

I want to know more about Euler characteristic, for instance. Is that so bad?

And, with the kind of time I have (unlike lucky you), I can't really study NT at the same time, can I?

Also, @Balarka, I'm sorry for my part in the argument we had.

@Huy Oh, I showed my mom that brilliant video I linked yesterday. :)

Gato

@Hippalectryon tu fais des synthèses de document en anglais ?

Hippalectryon

@Gato oui

Gato

@Hippalectryon des conseils à donner ?

Hippalectryon

@Gato Pas vraiment, à part de faire une sorte de tableau récapitulatif de chaque document

Ca permet de faire facilement des liens entre les documents, de trouver les grandes parties

Gato

@Hippalectryon Ok, je vois, merci

Hippalectryon

10:25 AM

@Gato Aussi, la conclusion doit être très succinte (3-4 lignes)

Pas besoin de faire une ouverture

Gato

@Hippalectryon ah ok, merci :D

Chris's sis the artist

10:36 AM

Still drinking champagne and celebrating here! :-)))))

@Hippalectryon ^^^

Hippalectryon

@Chris'ssistheartist :-)

Chris's sis the artist

@Hippalectryon :-)))

Agawa001

dinking too much can cost you your brain cells

going to bath now, it helps me making new ideas

Huy

11:07 AM

@SohamChowdhury: What video? ö.ö

Remember me

11:24 AM

Hello@Huy

Huy

hi

Remember me

3

Q: Nonexistence of local isometry between equidimensional Riemannian manifolds

Recall that all inner product spaces of the same dimension are isometric. For example, if $(M,\mathrm{g})$ and $(N,\mathrm{h})$ are Riemannian manifolds of the same dimension, then $(T_pM,\mathrm{g}_p)$ and $(T_qN,\mathrm{h}_q)$ are isometric inner product spaces. Let $\beta:T_pM\to T_qN$ be a (...

differential-geometry riemannian-geometry inner-product-space isometry

These kind of questions are rarely present in the hot network question list

Huy

?

Remember me

?@Huy

Huy

If they were frequently present, they'd be duplicates and hence closed, no?

Gato

11:28 AM

@Chris'ssistheartist why ?

Chris's sis the artist

@Gato Read the comment I posted it yesterday and that was starred here. :-)

Remember me

But people think of question like "what is the proof that a negative number exists" and what not... Someone should also ask questions which are not just thought from anyplace but which show some research and effort behind them @Huy

Huy

@Rememberme: Can you prove that a negative number exists?

Remember me

Negative numbers are just extension of the natural numbers which can be constructed using peano axioms I assume @Huy

Gato

@Chris'ssistheartist about euleur sums ?

Euler *

Huy

11:31 AM

Do you often finish your proofs with "I assume", @Rememberme?

Chris's sis the artist

@Gato Yeah, I calculate them all by simple tools of the classical real analysis.

Remember me

No since I dont want to think about it I just wrote it like that @Huy

Do you mind me asking you a question @Huy?

Huy

Sure.

Remember me

Who is that small baby in the picture in your profile.... he/she is really quiet @Huy :)

Huy

@Rememberme: That's me, obviously. Just a few years ago.

Remember me

11:34 AM

Few?

Gato

@Chris'ssistheartist and it was unknown ?

Remember me

Doesn't seem so

Chris's sis the artist

@Gato Well, are you aware of any paper where all those series are done by simple solutions of the classical real analysis only? I'm not aware of anyone. I might be the first one that managed to do this, and major part of them will be in my book (maybe even all).

Gato

@Chris'ssistheartist I havent's seen this sums no, but i am not a sums addict :p. then, I must say congrats :))

Chris's sis the artist

@Gato Thanks! :-)

Gato

11:39 AM

@Chris'ssistheartist and what are you going to put in your book ?

Chris's sis the artist

@Gato Well, it will be a collection of problems and solutions about integrals, series and limits, major part of the problems being created by me, coming naturally from my own research.

Soham Chowdhury

@Huy this one

Gato

@Chris'ssistheartist ok cool, and did you find a publisher ?

Chris's sis the artist

@Gato Up to 500 problems with solutions.

@Gato Yeah, I also received a proposal from a publisher, not from my favourite one.

Gato

@Chris'ssistheartist be sure, I will buy it :)

Remember me

11:42 AM

Hello,soham

Look at this:

Gato

@Chris'ssistheartist and then we are going to know your real name ? :P

Remember me

135

Q: Mathematical "urban legends"

When I was a young and impressionable graduate student at Princeton, we scared each other with the story of a Final Public Oral, where Jack Milnor was dragged in against his will to sit on a committee, and noted that the class of topological spaces discussed by the speaker consisted of finite spa...

ho.history-overview

Look at the first answer

Huy

@Rememberme: math.stackexchange.com/questions/28885/…

Chris's sis the artist

@Gato Well, I wouldn't like to talk here about my real name, and probably I won't say anything if you ask me about this, but you will recognize that book is mine once is published. :-)

Remember me

Yes I got that from your answer @Huy

Soham Chowdhury

11:44 AM

@Rememberme I've read almost all the top questions on MO and MSE :P

Remember me

The first answer is just epic!!!!

Chris's sis the artist

@Gato I prefer to remain an anonymous here.

Gato

@Chris'ssistheartist but how can we find your book then ?

Amazon ?@Chris'ssistheartist

Chris's sis the artist

@Gato Hope so, and I also hope it will have a good price for any buyer. I intend to show a meganetwork of relations between amazing integrals, series and limits, not only to calculate them separately.

Gato

@Hippalectryon perhaps Hippa will find the book for me :P

Chris's sis the artist

11:47 AM

The amazing thing is to use them all once you solve them and attend more and more amazing stuff using the previous tools.

The thing with solving a question and then putting it aside and let the dust on it it's a very bad thing. I always need to use what he have already proven to get greater and greater results.

Soham Chowdhury

@Rem:
The following story is a bit strange to be true, but we all believed it as students, and I think I still do believe that a somewhat weaker version of events must have indeed occurred.
Michael Maschler (most famous in Israel as author of the standard math textbooks for middle-schools and high-schools) was in the middle of teaching an undergraduate course- I think it was Linear Algebra- when one afternoon he walks into the lecture hall and announces the discovery of a new class of incredible Riemannian symmetric spaces with incredible properties, missed by Elie Cartan. The undergrads ha…

Gato

@Chris'ssistheartist when it will be available, I will talk with the librarian to buy it for the university :)

Chris's sis the artist

There is nothing to throw, no problem at all, all these can be turned into precious tools for future problems. This is my view on the solved problems.

@Gato OK :-)

Remember me

haha@Soham

Chris's sis the artist

Then once you have a problem solved, you redimension it, endow it with, say, new parameters, you try to solve them in different conditions, the idea is to develop all into sophisticated tools.

Who only cares about solving a poor problem? That's not me. The real objectives have to always be great and for that you need those d*mn sophisticated (or better say, well developed) tools.

So, work extremely hard on that, work extremely hard on that and once again, work extremely hard on that ...

That's the key imho.

Soham Chowdhury

11:55 AM

@Rem, my favourite is this one:

One of the homework assignments had a question of the form:
"Let G1 be the group …, and G2 be the group … Prove that G1 and G2 are isomorphic."
One of the papers submitted had an answer "We will show that G1 is isomorphic..." and some nonsense, followed by "Now we'll show that G2 is isomorphic..." and more nonsense.

Huy

@SohamChowdhury @Rememberme: Check out the post about math puzzles, some of them were really cool.

@SohamChowdhury: Read the comments for the post you just quoted, those are amazing.

Soham Chowdhury

I have.

Remember me

haha

Gato

@Chris'ssistheartist always the key but not the only one, and rather difficult too ;)

Remember me

The set of all limit points always closed right?

Hippalectryon

12:21 PM

@Chris'ssistheartist Yeah that's hard :/ see @TedShifrin's books. Publishers sometimes set really high prices

Chris's sis the artist

@Hippalectryon Since I'm not a professional, they might not set such a price.

Hippalectryon

Let's hope so :-)

Chris's sis the artist

@Hippalectryon When you have time tell me some of your ideas about how such a book should be written. Well, things about anything related to such a book.

Hippalectryon

Ok, I'll think about it

Chris's sis the artist

@Hippalectryon OK, thanks! :-)

Mew

12:29 PM

hi can someone help with this quesitn

how can i show x + 1/x is always bigger than 2 for positive x

what's the simpliest way

i know it can be done with calculus

but how else?

Hippalectryon

@Mew Why do you want another way ?

Mew

because i was reading a book that said since x+x^-1 is more than 2

so matter of fact

I wondered if it was obvious

without perfomring a calculation and if so how

Hippalectryon

It is rather direct. Multiply both sides by $x$ you get $x^2-2x+1\ge0$. Isn't that clear ?

Mew

/

?

Soham Chowdhury

In fact, $x + 1/x \ge 2$, not $>$.

Mew

12:35 PM

yes

Soham Chowdhury

Assume the opposite.

Then $x^2 - 2x + 1 < 0$.

Hippalectryon

@SohamChowdhury That's not the opposite. The opposite would be $x^2-2x+1<0$ for one given $x$

Soham Chowdhury

So $(x-1)^2 < 0$, so . . . ?

@Hippalectryon $\exists x . x+1/x < 2$, yes.

Hippalectryon

You mean $<2$ ?

Soham Chowdhury

But it's astounding how many people never learn how to negate quantified statements.

Ach, yes.

Hippalectryon

12:37 PM

:-)

Mew

alright i get it

thanks

Soham Chowdhury

Good. :)

Hippalectryon

You don't need to negate it though. As I said above, just look at $x^2-2x+1\ge0$, which is clear.

Mew

yeah

i dont think negating is necessary

Chris's sis the artist

1:11 PM

@Hippalectryon Can you believe I didn't attend any drop of mathematics since yesterday? :-) I simply don't wanna think of anything mathematical. :-)))))

Hippalectryon

@Chris'ssistheartist You're gonna be sick, lol

Chris's sis the artist

@Hippalectryon lolllll :-)

Hippalectryon

Well, it's good to take a break from time to time

Chris's sis the artist

Yeap. :-)

I'm out to watch a movie. :-)

Agawa001

@Hippalectryon the point is, i do maths in my leisure, definition of a break differs with people.

Hippalectryon

1:20 PM

@Agawa001 Still, you take a break from something you usually do.

That's pretty general

Agawa001

my beak is those few minutes i take hike on my feet or ride my bike, smell fresh air and bathe in sea (when it s summer) , i dont usually go to bar or play any thing entertaining

i just made a mathematical function which spares me n*n calculations, i m looking forward to see results on projecteuler

Ted Shifrin

@StanShunpike You'll have to ask me in person what your question is. I'm not sure I get it. No, there's no name for "almost a transpose." :P

Huy

1:40 PM

@TedShifrin: There's many examples of "what is not a submanifold", e.g. we look at $f: S^1 \to \mathbb{R}^2$ given by $f(x,y) = (x,xy)$ which produces a figure 8. The map $f$ is a proper immersion but clearly not injective. This shows me that this specific map $f$ is not an embedding. But how can I show that in general, the figure 8 is not an embedding in $\mathbb{R}^2$ or that it is in general not a submanifold?

Ted Shifrin

Good exercise for you @Huy: Prove that any embedded $k$-dimensional submanifold in $\Bbb R^n$ must locally be a graph of a smooth function over one of the standard $k$-dimensional planes in $\Bbb R^n$. (So in $\Bbb R^2$, a graph over either the $x$-axis or the $y$-axis.)

Huy

@TedShifrin: Any submanifold is embedded by the inclusion map, right?

Ted Shifrin

Any embedded submanifold, yes.

Do you need a hint for the exercise?

Huy

I think we did a similar result and I'm trying to remember it.

@TedShifrin: This only holds in $\mathbb{R}^n$?

Ted Shifrin

Well, my conclusion only makes sense in $\Bbb R^n$. You can make sense of it appropriately in a chart on a more general manifold, yes.

skill patrol

1:59 PM

If 0 times any number is 0, what logical principle has been used on this statement to say that 0 times no number is nonzero? @TedShifrin is it The law of non-contradiction?

Ted Shifrin

I have no idea ... I don't know these basic logic terms.

Huy

@TedShifrin: Using your statement, the reason it cannot be an embedded $1$-submanifold is because in any neighbourhood, the intersection point cannot be the graph of a function over an axis, right? Just making sure I understand your statement correctly.

Ted Shifrin

Correct, @Huy. But it reduces to a finite check ... That's the beauty of this result. Same thing with something like $y^2=x^3$.

OK, we have gorgeous weather, so I'm going for a walk. BBIAB.

Huy

Have fun!

skill patrol

later pal

Mary Star

2:04 PM

Hello!!

Is someone of you familiar with theoretical computer science?

Are you familiar with CS @Agawa001 ?

Agawa001

counter strike ? no, C sharp ? lil bit

evinda

@DanielFischer Hi!!! Can I ask you something?
Does $x-y \not\equiv 0 \mod 3$ imply that $y-x \not\equiv 0 \mod 3$ ?

Agawa001

Computer science ? be more precise

evinda

@SohamChowdhury What do you mean?

Agawa001

@evinda yes

Daniel Fischer

2:12 PM

@evinda Yes, $a$ is a multiple of $m$ if and only if $-a$ is a multiple of $m$. Set $m = 3$.

Agawa001

and the invese is also true

Mary Star

Are you familiar with Rice's theorem and reduction? @Agawa001

evinda

@Agawa001 @DanielFischer Great!!!And from this we have that the relation:
$xRy \Leftrightarrow x-y \not\equiv 0 \mod 3$ is not antisymmetric, right?

Agawa001

@MaryStar hmm sorry, im afraid i cant help in this

Mary Star

Ok... no problem... @Agawa001

Daniel Fischer

2:18 PM

@evinda Well ... you need to show that there are $x\neq y$ with $xRy$ to conclude that. Not that that is difficult.

evinda

@DanielFischer A ok.. We can pick 6 and 9, right?

Daniel Fischer

@evinda Err, but $6-9 \equiv 0 \pmod{3}$.

evinda

@DanielFischer So do we want x and y such that $x \not\equiv 0 \mod 3$ ?

Daniel Fischer

@evinda Yes, we want $x \neq y$ such that $xRy$ - and then also $yRx$ - to deduce that $R$ is not antisymmetric. For then we have $xRy \land yRx$, yet $(x,y) \notin \Delta$, so $R$ is not antisymmetric. [If your definition of antisymmetry is that for no $x,y$ we have $xRy$ and $yRx$, then we don't need the $x\neq y$ constraint, but in this case $xRy$ implies $x\neq y$.]

evinda

This is my definition:

If M is a set $R \subseteq M \times M$ , then R is antisymmetric, if it holds

$\forall x, y \in M: xRy \and yRx \Rightarrow x = y$ @DanielFischer

$x-y \not\equiv 0 \mod 3$ and $y-x \not\equiv 0 \not\mod 3$

$4-5 \not\equiv 0 \mod 3$ and $5-4 \not\equiv 0 \mod 4$ but $5 \neq 4$.

So can we pick $x=4,y=5$ ? @DanielFischer

Soham Chowdhury

2:35 PM

@evinda Well, you were talking about a Greek dance, and I linked you to something with a nice Greek lute player. :)

evinda

@SohamChowdhury Could you relink it? I didn't see it.

Soham Chowdhury

@Rememberme Hey, I was just fighting with this very problem. What a coincidence!

Daniel Fischer

@evinda Yes, we can pick $4$ and $5$. In fact we can take any $x,y$ with $xRy$, since $R$ is symmetric (but irreflexive).

Soham Chowdhury

Efrén López - Perdesiz Gitar Taksim (Fretless Guitar Taksim)

►

@Rem, I think this works only in Hausdorff spaces, but I'm not sure yet because I don't properly know what those are. It works in metric spaces all right AFAIK.

evinda

Nice :D @SohamChowdhury

@DanielFischer Thank you very much!!!

Huy

2:50 PM

@SohamChowdhury: Pretty much all bow instruments are without frets?

evinda

Any news? @SohamChowdhury

skill patrol

If 0 times any number is 0, what logical principle has been used on this statement to say that 0 times no number is nonzero? @DanielFischer is it The law of non-contradiction? I was thinking along the lines of if all real numbers have the property 0 times any real number is 0, then no real number can not have this property, for that would be a contradiction.
It is impossible to have a property and not have the same property at the same time.

Huy

@skillpatrol: I think you mean "not have the same property"

skill patrol

@Huy yes, thank you :-)

@TedShifrin wb

Ted Shifrin

Thanks, skull. Did you decide on the logic term?

Heya @DanielF :)

@skull: You're wanting to say that $\forall x\, P(x)$ implies $\not\exists x \,\sim P(x)$.

Huy

2:58 PM

This might be the first time I see @skillpatrol doing something maths-related in this chatroom.