Transition from something to nothing

  • Thread starter nate808
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  • #1
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This may sound stupid, but it has always confused me. If you take a line and break it into infinitely smaller pieces, you would have miniscule lines while approaching infinity, yet at an "actual" infinity what is left is just points. What bothers me is, what happens inbetween. Is there some transition from lines to points, or is it just accepted as two separate entities?
--Thanx
 

Answers and Replies

  • #2
tmc
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this is like asking what happens between the number 999999999 and the number infinity...
 
  • #3
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ya but aren't there different sized infinites, with cardinality and things of that nature? I mean i will concede that it is a stupid question, but for some reason i just imagine that there could be things like cantor dust, or fractional dimensions, but I guess not.
 
  • #4
Integral
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Get past the concept of "at infinity" do not think it of something that can be reached, instead think of it as a destination which cannot be reached. Thus, the answer to your question is that you are always in that "in between" region.
 
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  • #5
HallsofIvy
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nate808 said:
This may sound stupid, but it has always confused me. If you take a line and break it into infinitely smaller pieces, you would have miniscule lines while approaching infinity, yet at an "actual" infinity what is left is just points. What bothers me is, what happens inbetween. Is there some transition from lines to points, or is it just accepted as two separate entities?
--Thanx

Your basic concept of "take a line and break it into infinitely smaller pieces" is meaning less. You would have to describe exactly what limit process you are using. Different limit process will give different results.
 

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