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6:34 AM
@LeakyNun You may be interested in my axiomatization of projective space:
A projective space is a structure with lines and points and planes in which all the following axioms hold:
(1a) Any two distinct points are contained in a unique line.
(1b) Any two distinct planes intersect at a unique line.
(2a) Any two distinct lines intersecting at a point are contained in a unique plane.
(2b) Any two distinct lines contained in a plane intersect at a unique point.
(3a) Any line contains three distinct points.
(4a) No line or plane contains all points.
Note that (3a) and (4a) are their own duals, so any projective space obeys duality.
how are they their own duals?
Sorry they are not their own duals, but their duals can be proven from the rest.
I mis-quoted myself from my own reference haha..
Axiom (3a) is strictly stronger than the following condition:
(3’a) Any line contains two distinct points.
If axiom (3a) is replaced by (3’a), then Desargue’s theorem is no longer true for general projective spaces.
Axiom (4a) is strictly weaker than the following condition:
(4’a) There are points such that no line or plane contains them all.
Axiom (4’a) implies that there are at least four such points and hence at least four planes and six lines, while axiom
(4a) allows the projective space to have less than two points and less than two planes as long as it has no lines.
wait, you can prove Desargue from those axioms above? (don't give me any hints, still trying to figure out a proof)
Yes from the 6 axioms I gave alone, you can prove Desargue's theorem.
6:40 AM
My proof is not that short. About 50 lines each of which is like 5 deductive steps, and throughout using syntactical symmetry considerations.
I like challenges
I basically designed the axiomatization to be barely strong enough for the proof to go through. That was during a course where I was given an assignment which was to prove that Moulton's plane is a projective plane that does not satisfy Desargue's theorem. And I realized that the critical failure was due to (3a), and that ( Moulton's plane plus a point outside plus the naturally induced lines and planes ) satisfies all the axioms minus (3a).
@LeakyNun Do you need the precise statement of Desargue's theorem?
@user21820 no
is your proof constructive?
@LeakyNun Well I'm not sure you will find a precise version of the theorem statement online, and of course it's necessary to exclude some degenerate cases.
alright, let's hear your statement then
6:53 AM
In any projective space:
Given distinct points A,B,C,D,E,F such that A,B,C are non-collinear and D,E,F are non-collinear:
AD,BE,CF are distinct concurrent lines iff AB∩DE,BC∩EF,CA∩FD are distinct collinear points.
I see
@LeakyNun I definitely used LEM all over. In my proof structure it is explicitly used for equality of points and planes, but I won't be surprised if I used it for lines as well. (I'd have to read my proof to check that.)
2 hours later…
8:31 AM
@LeakyNun Have you proven it yet? =)
2 hours later…
10:05 AM
Anyone over here has good programming skill?
(I am in desperate need of it .... Need to verify if some kinda pattern emerge)
Or is there another chat room better for such kind of favors?
@AnantSaxena StackOverflow has a chat-room.
AH ... ohk ... thanks :D
But if you want to do anything with programming, the best and only way to do it right is to learn programming yourself.
It's not hard. I recommend Python.
I know ... It was taught to me as module and at the time my impression was inelegant and I want nothing to do with it ... But now I realize its importance
Haha it's never too late. Especially since you have had a bit of experience with it before, it should be quick to pick up again.
10:14 AM
yea ... I should but time seems so scarce these days :(
@AnantSaxena If you have any problems learning Python or another common programming language, you can ask here, because a couple of us know how to program quite well.
also I cant find the room you talked about in overflow
@AnantSaxena Let me search.
thanks :)
Interesting; I thought there was one but I can't find it.
So perhaps there is none.
10:18 AM
nooo ... Now how will I get/(convince) someone that the idea is worthwhile to program:
P.S: If your having a look id recommend you look at the algebraic representation
@AnantSaxena I honestly also have no interest in your idea, because I do not expect any unusual pattern concerning primes to show up.
Law of small numbers may refer to: The Law of Small Numbers, a book by Ladislaus Bortkiewicz Poisson distribution, the use of that name for this distribution originated in the book The Law of Small Numbers Hasty generalization, a logical fallacy also known as the law of small numbers The tendency for an initial segment of data to show some bias that drops out later, one example in number theory being Kummer's conjecture on cubic Gauss sums Strong Law of Small Numbers, an observation made by the mathematician Richard K. Guy: "There aren't enough small numbers to meet the many demands made of them...
But you are welcome to learn programming after which you can try finding patterns to your heart's content.
Alright can I ask your help in python then while I do it myself?
Of course!
ah .. ohk
thanks :D
crap ... I have to study :P ... when will you be available next online?
like after 3/4 hours etc?
I'll ask u then @user21820
Well there's no hurry. Just take your time. There should be ample Python tutorials online to help you get started.
And then you can just ask here and probably someone might help you even if I'm not around.
@AnantSaxena: Someone in another chat-room pointed me to here and from there we see:


Room rules: sopython.com/chatroom Code formatting guide: tinyu...
@YokaiTheMonster: Hello and welcome!
This is where it began. =)
10:34 AM
Thank you very much @user21820 :)
You can come here if you're bored. =)
ha ha sure :)
@KulsDroid :D
I noticed. He follows you around, eh?
ha ha ha he
@KulsDroid: Welcome to this room too!
10:37 AM
yeah @user21820 he is my friend :)
thanx @user21820
Haha @user21820
Nice to meet you.
Nice to meet you too mate!
same here :)
Okay I shall go off and finish an answer on Math SE now.
See you around!
10:40 AM
Sure thing! Bbye
3 hours later…
2 hours later…
3:44 PM
Q: $\text{Understanding the bounds that arise from the compact subset }$ $E_{r}=\overline{\Bigg(\bigcup_{z \in E}D(z,r) \Bigg)}$

ZophikelIn the text "Function Theory of One Complex Variable Third Edition" by Robert E. Greene and Steven G. Krantz i'm having trouble understanding how the bounds were constructed from the compact set $E_{r}$ in $\text{Corollary 3.5.2}$, the initial proof to the Corollary is developed in $(2)$, while t...

^ Anybody got an answer ? been stuck on this one for a while ?
6 hours later…

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