Exploring Unbounded 3D Space: Can It Exist?

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In summary, the conversation discusses the concept of unbounded 3-dimensional space and provides examples such as the surface of a 4-dimensional sphere and the analog of a torus. The term "unbounded" may be subjective, as some may consider a 3-dimensional sphere to be bounded but having no boundary. It is important to define the term "bounded" in order to have a clear understanding of the concept.
  • #1
touqra
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Can there be any unbounded 3 dimensional space? For example, for a 2-dimensional space, we have an unbounded surface that resides on a sphere.
How about three-dimensional space?
 
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  • #2
Sure. For example, the surface of a 4-dimensional sphere!


(PS: I'm not sure if "unbounded" is the word you're looking for... though it might be)
 
  • #3
R3 is unbounded.
Maybe he is looking for "finite but unbounded".
Another example is the analog of a torus (The Asteroids topology :tongue2: ).
 
  • #4
Now this is what has confused me, surely an n-sphere is bounded as a metric space, I think the correct matehamtical term is 'boundaryless' i.e. a manifold without boundaries.
 
  • #5
The example he gives (surface of a sphere) is what I would call (perhaps "paradoxically) "bounded but having no boundary".

That is, the set of all possible distances between points has an upper bound but there is no boundary: points such that every neighborhood contains some points in the set and some points not in the set.

Of course, there exist 3 dimensional bounded sets that have no boundary- but you have to imagine them embedded in 4 dimensional space. The surface of a 4-sphere is an example.
 
  • #6
Actually now I think a little more, boundaryless and compact is probably what the OP was looking for.
 
  • #7
it always helps to define your terms. i.e. does "bounded" mean not very big, or having an edge?
 

1. Can unbounded 3D space actually exist?

This is a highly debated topic among scientists and philosophers. Some argue that the concept of unbounded 3D space is purely theoretical and cannot be proven or observed. Others believe that it is possible for space to be infinite and unbounded.

2. How do we explore unbounded 3D space?

Exploring unbounded 3D space would require advanced technology and spacecraft that can travel at incredibly fast speeds. It would also require a detailed understanding of the laws of physics and how they apply in an infinite space.

3. What are the implications of unbounded 3D space?

If unbounded 3D space does exist, it would challenge our current understanding of the universe and raise questions about the nature of time and space. It could also have significant implications for space exploration and the search for other habitable planets.

4. Is there any evidence for unbounded 3D space?

Currently, there is no concrete evidence for the existence of unbounded 3D space. However, some mathematical theories and observations of the cosmos suggest that it is a possibility.

5. How does the concept of unbounded 3D space relate to the Big Bang theory?

The Big Bang theory suggests that the universe began as a singularity, expanding and creating space as it grew. If unbounded 3D space exists, it would mean that the universe is infinite and has always existed, challenging the idea of a singular beginning.

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