1. Originally Posted by Zelos
proving 0,999.....=1 is quite simple
x=0,999...
10x=9,9999...
9x=9,9999...-0,9999...=9
therefor x=1
Yes.. but if you look you are making a number of assumptions. You need to be able to justify each statement.

But yes I am sure everyone and their mothers know this proof   2. there isnt any assumption exept that 9=9 anbd 10=10 and .... means its repeating  3. endless is undefinable because endless is unimaginable..

when we go smaller than atoms with calculation (by now) we can define it as true.. so 0,99999 isn't 1 but 0,999999999999999999999999 is 1.

that until smaller particles have been found..

1/3 * 3 is obviously 1..
1 * 3/3 is also 1..
0.333..+0.333..+0.333.. is 1 because one of the 1/3 has a 4 instead of a 3.

it's like electromagnetism... the combining electron is nowhere and everywhere.. it connects them..

now stop argueing!!  4. endless isnt undefinable. definition, no matter how much you can write it on, digital or analog, you allways have to write more.  5. Define a point.  6. 0 dimensions  7. LOL.

We could keep going. Define zero dimenstions.

Basically a point is undefined. It can't be. However a point is the building block of a lot of things, even 1-dimenstion.  8. a real point have 0 dimensions, a dimension is the degree of freedom objects have, 0 means no freedom, no movement. while 1 dimension means 1° of freedom, you can move back/forth no more, and so on for a infinite amount of dimensions  9. Originally Posted by Absane
Basically a point is undefined.
A point is defined, and has meaning only in the context of its definition. There are no geometric points in the real world.

However a point is the building block of a lot of things, even 1-dimenstion.
Just as points have no existence in the real world, neither do geometric lines.  10. Originally Posted by Zelos
a real point have 0 dimensions, a dimension is the degree of freedom objects have, 0 means no freedom, no movement. while 1 dimension means 1° of freedom, you can move back/forth no more, and so on for a infinite amount of dimensions
For one... we aren't talking reality. Two, those are just properties of a point.

The point is (pun intended) a point is a basic object, so it has no definition within mathematics. Just like axioms have no proof within the system.

Everyone knows what a point is, but defining it is impossible.  11. 0 dimensional object
dimension is a degree of freedom
freedom is the amount it can move  12. Originally Posted by Absane
The point is (pun intended) a point is a basic object, so it has no definition within mathematics. Just like axioms have no proof within the system.

Everyone knows what a point is, but defining it is impossible.
I do not think that a point is an object. It does have a definition within mathematics, at least within geometry. Axioms have no proof, but points are not given by axiom, but by definition. No one knows what a point is except by defintion, which is very easy. I am not sure what you mean when you say that it is impossible to define a point. Without a definition, then it would have no meaning, such that no one would know what a point is.  13. Originally Posted by Zelos
0 dimensional object
dimension is a degree of freedom
freedom is the amount it can move
You don't think an object in 0D can move? It can. Movement can be static or rotational.It's still a point.

Remember.. we are talking about a geometrical point. And a point is a BASIC object in mathematics... so it cannot be defined.

To define a point, you need to list all of it's properties and be absolutely sure that nothing else can be said about it. You also need to use objects/properties that do not presuppose the existance of a point that created these objects/properties. Dimensions are composed of points. 0D happens to have one unique point, but you could easily say it has an infinite number of points (we just won't identify that they are all the same point).  14. Originally Posted by Hermes
I do not think that a point is an object. It does have a definition within mathematics, at least within geometry. Axioms have no proof, but points are not given by axiom, but by definition. No one knows what a point is except by defintion, which is very easy. I am not sure what you mean when you say that it is impossible to define a point. Without a definition, then it would have no meaning, such that no one would know what a point is.
Well every topic in mathematics works by building on assumptions and undefined terms. You need to start somewhere.

Saying that without a definition we would not know what a point is and it has no meaning is silly. That is analogous to saying that without proof of axioms, we don't know that mathematics works. Well we don't know that these axioms are contradiction free because we cannot prove them. However, they have worked good so far.

What are the basic building blocks of mathematics that define a point? If you can answer this... I will shut up   15. Originally Posted by Absane
What are the basic building blocks of mathematics that define a point? If you can answer this... I will shut up
I am not sure what your question is. What do you consider to be a building blocks of mathematics? Are you asking for the fundamental constituent building blocks of the point? I doubt that. So, what are you asking for. I am not sure of your point.  16. Originally Posted by Hermes
I am not sure what your question is. What do you consider to be a building blocks of mathematics? Are you asking for the fundamental constituent building blocks of the point? I doubt that. So, what are you asking for. I am not sure of your point.
Absane is talking about the philosophical problem of infinite definition descent : for example the idea of "set" is left undefined in mathematics, we talk about the properties of sets (and classes to be more correct) with out every actually defining what those things are. You can map the idea of a "point" onto any structure you want, for example in a function space functions make up the "points".  Bookmarks
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