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Going at The Speed of Light

  1. Feb 17, 2009 #1
    I know it is impossible(for now:wink:), but if we use the mathematical proofs that any non-zero number with a finite decimal notation has a counterpart with trailing 9's. So, unless that is not always true, then wouldn't anything moving at 99.999...% (supposing we reach that somehow)the speed of light be actually moving at c? Remember the proofs, 0.9999....=1

    Correct me please, something is definitely not right.

    regards,
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  2. jcsd
  3. Feb 17, 2009 #2

    mathman

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    The problem is physical not mathematical. In order to get to the speed of light you need infinite acceleration.
     
  4. Feb 17, 2009 #3

    HallsofIvy

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    Yes, 0.9999...= 1. Therefore you cannot travel at either c or 99.999....% c. They are just different ways of saying the same thing.

    Your question is precisely the same as "I know it is impossible to go at c, but suppose we used the letter a and let a= c. Wouldn't anything going at a be actually moving at c?"
    Yes, and that is why you cannot travel at c or a?
     
  5. Feb 17, 2009 #4
    Thank you for your explanation HallsOfIvy, learning is the greatest experience:biggrin:

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  6. Feb 17, 2009 #5
    On second thought, where do we impose the limit of speed when getting close to c? It is common knowledge that 99.999... extends to infinity, but what is infinity -1? Where do we put the limit? In other words what is the fastest one could go? Going at 99.999...%c implies infinite energy required, so where must we stop, supposing we had an energy source equal to infinity -1?:uhh: Hopefully I was clear.

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  7. Feb 17, 2009 #6

    jtbell

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    You never stop accelerating. You just keep on getting closer and closer to c, approaching it more and more slowly.
     
  8. Feb 17, 2009 #7

    Vanadium 50

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    A few points. One is that 0.9999... and 1.0000... are two different ways of writing the exact same number. (Like Halls of Ivy said). In this way they are no different than 1/2 and 0.5 are.

    The other is that (infinity minus one) is not a number.
     
  9. Feb 17, 2009 #8
    Of course not, it was just an example to try to explain what I meant, sorry about the sloppiness. I guess that's a good way to think about it, you keep accelerating more and more slowly, never reach c, but use up more, and more energy. Thanks for all the clarifications!
     
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