/sci/ - Science & Math

An entity of zero dimensions existing within a volume of one or multiple dimensions.

(x,y)

I hate this board.

>>4299535
Zero dimensions? How is this possible? Only the vector space of the zero vector has dimension zero.

>>4299537

...or (x,y,z)

>>4299537
This is a point in a two dimensional structure. I was asking for a general definition.

A point is an element of a vector field.

>>4299544

What are dimensions? How does that make any sense to be a dimension, do we even know they exist?

What are words, please define all words using non-word words.

>>4299548
Neither does your post give a general definition.

>Mathematically speaking, what is a "point"?

Be more precise. In ℝⁿ or ℂⁿ it's a order n-tuple of numbers in that set: P=(X₀,X₁,X₂,...)

An element of a topological space.

A point is that, which has no part

>>4299556
ordered

>>4299551
An element of a vector FIELD? A vector field is a vector valued function, not a set. And elements of vector SPACES are called vectors, not points. A point doesn't need operations like addition or multiplication.

>>4299552
Mathematics needs rigorous definitions.

>>4299556
I cannot be more precise. I am simply asking for the definition of a point, generally speaking. Don't come up with special cases.

>>4299559
Any set can be a topological space. Would you consider arbitrary elements of arbitrary sets as points?

>>4299560
How do you know you cannot split up a point into smaller points?

My fellow, a point is a mathematical abstraction of something infinitely small.

I think Decartes was the first to think about it (correct me please gentleman).

After creating the natural numbers set, we can represent graphically something like U = N x N x N ... x N (x is the cartesian product). We can say that the set O is a isomorphism of U and that it is a set of ordered (n-tuples). A point is the graphical representation of a ordered (n-tuples) in a n-ortogonal axis space.

I think I am doing it wrong... Well there is some educated mathematician who can answer this?

>>4299544
>Zero dimensions? How is this possible?

What it means to have zero dimensions is that the entity has single, unique identifiable co-ordinates, and does not exhibit any variance along any dimension.

>What are dimensions?

Variable qualities.

In geometry, topology, and related branches of mathematics, a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics dealing with set theory, an element is sometimes referred to as a point.

>>4299577 Here.

I think we can take the words "space" and "axis" from the explanation, but that would make the explanation longer.

>>4299576
>How do you know you cannot split up a point into smaller points?
That is exactly the definition. What cannot be divided (has no part). Look up your Euclid, he got this covered.

>>4299564
>A point doesn't need operations like addition or multiplication.

This is why we have affine spaces.

>>4299577 Here.

>>4299589 Excellent!

Euclid! Of course!

Euclides have it defined geometrically.

Taken form wikipedia article

"Points are most often considered within the framework of Euclidean geometry, where they are one of the fundamental objects. Euclid originally defined the point vaguely, as "that which has no part". In two-dimensional Euclidean space, a point is represented by an ordered pair, (x,y), of numbers, where the first number conventionally represents the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y. This idea is easily generalized to three dimensional Euclidean space, where a point is represented by an ordered triplet, (x,y,z), with the additional third number representing depth and often denoted by z. Further generalizations are represented by an ordered tuplet of n terms, (a1,a2,...,an) where n is the dimension of the space in which the point is located."

I think it was some definition like that you were expecting. You can find it in any Real Analysis book first chapter.

>>4299577
>something infinetely small
Anything can be scaled to be infinitely small. That doesn't need to be a point. Although cartesian coordinates are useful, a point doesn't require them to exist.

>>4299578
You just shifted the problem by making it now impossible to define dimension.

>>4299587
>a primitive notion upon which other concepts may be defined
How can you define other things upon an entity that you still haven't defined rigorously?

>>4299588
I don't need an explanation, just a simple definition.

>>4299595
Unrelated to the concept of a point.

>>4299597
A triangle, a square or any other geometric object can be defined without resorting to coordinates. It has to be possible for points too.

>>4299576
Well, as long as you make it clear that you consider the set to be a topological space, I don't really see the problem.

A point is a ordered set (n-tuple) of a set that is the the Cartesian product with one or more different sets such that the nth element belongs to the nth set.

>>4299623
What is wrong with Euclid's original definition?

A point is the geometric form which can be no other smaller than it.

>>4299624
Points have to be definable without topology. Otherwise you couldn't operate on them in basic geometry.

>>4299626
Not again this highschool pseudo-definition. Read the thread and see why it's insufficient.

>>4299627
"That which has no part" is a philosophical description, not a rigorous definition.

>>4299640
How do you show then that not maybe one point is smaller than another one?

>>4299623
>implying a point isn't just an element in affine space
>implying geometry isn't a mere application of the theory of affine spaces

>>4299660
Please don't post in a math thread, if your knowledge doesn't go beyond highschool.

>>4299666
Maybe you should follow your own advice.

>>4299676
I came here asking for help. YOU obviously can't help me. Please stop derailing my thread now.

>>4299647

Ok I surrender.

But, at least my definition is concise.

>>A point is the geometric form which can be no other smaller than it.

If there is a point greater than other, than is not a point.

I sincerely don't know if this is true. But it makes some kind of sense.

>>4299608
>How can you define other things upon an entity that you still haven't defined rigorously?
How do you rigorously define a set ?

>>4299692
You are just rephrasing euclid's definition, which we already agreed on to be too vague.

>>4299698
This is another question. You can make a new thread about it. My thread is about points.

>>4299701

Then I guess I can't help you. It was fun though.

Good luck chap!

>>4299706
This was just to show that some objects do not or cannot have a satisfying and rigorous definition

>>4299742
This might be the case in philosophy, but here we are talking about mathematics, dude.

>>4299748
Yes, and in mathematics, there are basic things you cannot define (like a set or an element) which are called primitive terms because their definition would either be circular or use terms which would then have to be defined, just think about it, I'm not making this up.

>>4299788

Define opisafag mathematically.

>>4299795
<div class="math">(OP;fag) \in {(x,x) / x \in /sci/}</div>

>>4299788
Mathematics is not philosophy.

>>4299795
<div class="math"> (OP;fag) \in \{(x,x) / x \in /sci/ \} </div> ?

>>4299821
I'm probably being trolled but, for the last time, this is not about philosophy, it is about logic which is the very foundation of mathematics (and indeed philosophy but when you look at mathematics at this very abstract level, the difference is smaller than you think).

>>4299898
Of course it's not a about philosophy. This thread is about mathematics and mathematics has rigorous definitions.

>>4299902

http://en.wikipedia.org/wiki/Set_theory

http://en.wikipedia.org/wiki/Mathematical_constructivism

interesting

>>4299940
So what?

what the fuck guys. a point is an element of an affine space. done.

>>4299549
The definition (or lack thereof) is going to depend on the context. First you have to know what kind of geometry you're doing, and then what axioms you're using as a basis for the system, and then you can ask if and how points are defined.

>>4299967
>what geometry you're doing
There is only one geometry.

>>4299954
Shut up, we are talking about mathematics here, not highschool bullshit.

>>4299979
Trivially false: There were already two geometries mentioned in the first four replies:
>>4299537
>>4299548
And those are just the most well-known ones.

>>4299979

>>4299987
These are not geometries, dumbass. These are vector spaces. Geometry is a branch of mathematics. Now go on and tell me there is more than one branch called "geometry".

What a pointless discussion.

>>4299997
get!
also I see what you did there

>>4300000

>>4300010
>❤♡❤♡❤♡{King of /sci/}❤♡❤♡❤♡

A "point" is a primitive notion. It's an undefined concept upon which other concepts are defined, like an axiom in logic.

>>4300019
>an undefined concept

Keep your religion out of mathematics. Undefined stuff belongs to /x/.

A point is just another way of saying element of a set. So in R2 a point is any element e.g. (1 , 2) or (pi , e)

>>4300022
What's your point, OP?

>>4300019
>implying urelements in ZFC

>>4300023
I don't want examples, I want a definition.

>>4300022

http://en.wikipedia.org/wiki/Primitive_notion

Stop being a faggot and go get an education.

>>4300025
>implying any nontrivial math is done in ZFC

>>4300026
go fuck yourself, I gave you a definition. So your just a troll after all.

>>4300024
That he's a troll and that we all fell for it (or a very stubborn 12 year-old, go figure which one is worse..)

>>4300029
You might want to stay primitive, but I accepted civilization.

>>4300026

It's a primitive notion. It can't be defined in terms of other defined concepts. This has been said at least three times in the thread and you keep ignoring it, leading me to believe you're just a troll.

>>4300036
Your definition is nonsense. It represents the incomplete view of an uneducated highschooler who can't into real maths.

>>4300026
What this guy said: >>4299954

Anyone bumping this thread is an idiot.

>>4300041
Okay, now he's not even faking anymore

>>4300043
No, you are the troll claiming mathematics doesn't need definitions.

reported. saged. Hidden.

>>4300044
It seems, on the contrary, that you're the one that can't into basic algebra. A "true" mathematician would have at least said why he's wrong. All you're saying is "durr you suck let me troll some more". What don't you understand in "affine space"?

>>4300053
Tiens, depuis quand tu as un tripcode sécurisé? (Je sais que c'est pas vraiment le sujet du thread mais c'est pas comme si le thread n'était pas merdique pour commencer.)

>ITT

>>4300053
What the fuck? You cannot report me for asking a math question which you are too uneducated to answer.

>>4300054
Like already stated above, points don't require vector spaces.

>>4300061

>>4300060
depuis toujours il me semble, pourquoi?

>>4300064

Do you want a formal definition or some bullshit discussion with used and over used arguments from both sides?

>>4300061
Actually, it's more like this.

>>4300074
I want a fucking definition, you troll.

>>4300081
http://en.wikipedia.org/wiki/Point_%28geometry%29

>>4300070
J'avais jamais remarqué. En haut de ma page web il y a marqué que les tripcodes sécurisés sont pour les "jerks". Sans aller jusque là, quel est l'intérêt?

>>4300081

This is officially the worst thread on /sci/ right now.

>>4300090
Wikipedia sucks at math. They don't have a rigorous definition in there.
Don't we have some mathfags here on /sci/ who can explain it?

>>4300097
>Wikipedia sucks at math.
No, you do. How about you read every article on that page before posting anything in this thread.

>>4300110
I did. They don't have a rigorous definition there.

>>4300090
bah pour dire des conneries, mais être sûr que c'est bien moi qui les dis et pas qqun d'autre. Et c'est aussi un avatar, je lui associe ce que je veux, et si je veux dire qqch d'autre, je vide tout simplement la case "name". On est sur internet, et j'ai le contrôle de ce que je fais, alors je me gène pas!

>>4300122
Stop it. Keep your frenchfagging somewhere else. Not in my thread.

>>4300122
T'as oublié le sage, mon pote. Et en fait je veux juste savoir pourquoi tu utilises un tripcode sécurisé au lieu d'un tripcode normal. A moins de faire vraiment chier tout le monde sur /sci/ comme EK ou Deep&Edgy il y a peu de chances pour que tu te fasses cracker...

>>4300131
je vois pas ce que me coûte un # de plus! Mais sinon pour rien, en effet.

>>4300128
You'd be surprised by the number of Frenchfags on /sci/, especially tripfags. And this thread is utter shit anyway, it's not like speaking French can make it any worse. And I speak the language I want, don't be gelatinous.

>/sci/ doesn't know what a point is

Why doesn't their lack of mathematical education surprise me?

>>4300142
bref il est temps d'aller dodo, j'ai cours demain et pi je dois m'occuper de ma copine, à bientôt!

>>4300150
>mathgenius (not trolling)
>trolling

>>4300152
>copine
>prépa
J'espère sérieusement que vous ne faites pas ça, les gars.

>>4300150
Not all of us can be geniuses.

>>4300000
judging by your work in the putnam threads, you deserve this tripfaggot

I imagine by a point you mean a point in Kn

In which case it's an n-tuple representing a vector from the origin to a closed 0-dimensional subset of Rn

>>4302449
>didn't read the thread

A point is not a vector.

A point smallest label of a location.

>>4302461
Your post incoherent not sentence.

>>4302466
Enable em dashes.

(Pony Destroyed)