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Author Topic:   A layman's questions about universes
PaulK
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Posts: 17828
Joined: 01-10-2003
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Message 88 of 128 (117883)
06-23-2004 11:37 AM
Reply to: Message 79 by Buzsaw
06-23-2004 2:03 AM


To be a bit more precise an "open" bound is one which excludes the actual limit. So if we take the open interval (0, 1) on the Real Numbers we are looking at all Real Numbers greater than zero and less than one.
For any number in that range we choose we can find another that is closer to one and another that is closer to zero. One and zero are outside the range because we are using an open bound at each end and they are explicitly outside the interval.
If we choose 0.999, 0.9999 is closer to 1.
If we choose 0.001, 0.0001 is closer to 0.
In fact for any number, x, in the range that we choose (x+1)/2 will be closer to 1 and x/2 will be closer to 0.

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 Message 79 by Buzsaw, posted 06-23-2004 2:03 AM Buzsaw has replied

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 Message 91 by Buzsaw, posted 06-23-2004 12:20 PM PaulK has replied

  
PaulK
Member
Posts: 17828
Joined: 01-10-2003
Member Rating: 2.5


Message 93 of 128 (117899)
06-23-2004 12:30 PM
Reply to: Message 91 by Buzsaw
06-23-2004 12:20 PM


I'm just explaining the math. I guess the idea is that since the boundaries aren't in the interval they don't count. But I'm not sure of the reasoning there.
Nevertheless finite but unbounded makes perfect sense - the surface of a sphere is the usual example, but the perimeter of a circle works just as well. There are no boundaries on the surface or the perimeter - no matter how they are traversed neither includes an edge. The only "boundaries" are in higher spatial dimensions.

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 Message 91 by Buzsaw, posted 06-23-2004 12:20 PM Buzsaw has replied

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 Message 96 by Buzsaw, posted 06-23-2004 11:38 PM PaulK has replied

  
PaulK
Member
Posts: 17828
Joined: 01-10-2003
Member Rating: 2.5


Message 103 of 128 (118169)
06-24-2004 4:10 AM
Reply to: Message 96 by Buzsaw
06-23-2004 11:38 PM


The analogy is simple. Like the circle or the sphere (NOT a "disk" as you seem to think I said) the universe is curved in a higher spatial dimension. Thus the idea of the finite but unbounded universe states that the universe is curved back on itself in a higher spatial dimension, just as the one-dimensional perimeter is curved in a second dimension or the two-dimensional area is curved in a third. Where is the problem ?
And by the way might I suggest that the implication that analogies only apply to things that are identical to the objects in the analogy - rather than, well, analagous - negates the whole concept of an analogy. I trust that you never ever attempt to use analogies even to try to explain ideas since you think that they say nothing.

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