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Topologically ( not only using set theory ), we can arrange an infinite universe in such a way that it is contained by another infinite universe of the same dimension ? (as long as the contained universe remains coherent in its laws)
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Universe
- Thread starter Coreinvsbw
- Start date
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If you're asking if you can have a recursive structure of universes, all in the 3rd or 4th Dimension, then yes, you can.
OrangeFR
Username Only- 1,747
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If there are 2 infinitely sized 3d universes, you could not make them contain each other. Though it is possible for 2 to coexist in the same cosmology due to bulk space (a higher dimensional space in between them).
Edit: um, never mind my answer then, a thread mod likely knows more about this stuff than me.
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I mean, it's fiction; the author can technically write whatever they want. It would just end up making all the higher dimensions High 1-B+ or something around there.
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- Thread starter
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And would all the universes contained be of the same infinite size? and i want to know if it's topologically possible, otherwise, yes authors can do what they want to do
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Whether or not all the universes are infinite depends on the author. They can all be infinite; some may be finite.
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But let's say an infinite structure contains another infinite structure, then would the size of the container be Uncountable infinite?
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No, you can fit two infinities inside one another, without one being larger than the other.
For example;
(Natural Numbers); 1, 2, 3, 4, 5, 6...
(Even Numbers); 2, 4, 6, 8, 10, 12...
Technically, Natural Numbers contain Even Numbers; however, you can match them up one to one, making them equal.
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- Thread starter
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But can we apply set theory to a topological structure? It seemed to me that bijection in topology cannot be used to compare two structures
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