Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about infinity

  1. Dec 1, 2003 #1
    Hi. I'm a freshman in High school, and my algebra teacher gave me a problem. She said that .9 repeating = 1 Now apart from all the ways this didn't make sense to me, I thought of a way that might make it not work. If you were to put something like .0 [infinity of 0's] 1, wouldn't that be able to be added to .9 repeating, making 1? Correct me if I am wrong here, please. Thanks,
    Justin.
     
  2. jcsd
  3. Dec 1, 2003 #2

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

  4. Dec 1, 2003 #3
    There is a limit to how much we can measure. In fixing this limit we also fix our approximations. When there are infinites of nine we say that it is very close to one and hence approximate it to 1. We could approximate 0.999999999999999999999999999999999999999999999... to 0.9, but 0.9999999999999999999999999999999999999999.... is more closer to 1 than 0.9. Similarly, 0.0000000000000000000000000000000000000000001 is more closer to 0 than 1. Thus it is basically because there is a limit to our measurements and approximations that we approximate to te closest digit possible.

    Sridhar
     
  5. Dec 1, 2003 #4

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sorry, this is not correct. [itex]0.\overline{9}[/itex] is not approximately 1, it is absolutely 1. Remember, I'm not talking about a lot of nines, I'm talking about an infinite number of nines. That's a whole different bucket o' spaghetti.

    - Warren
     
  6. Dec 1, 2003 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I know it is hard to accept but even teachers are right ocassionally! The problem with you idea is that you can't have an "infinite number of 0s" and then put a 1 on the end. With an infinite number of 0s there is NO end.

    A non-terminating decimal such as 0.99999... is DEFINED as the limit of the sequence .9, .99, .999, .9999, etc. and that limit IS 1.0.
     
  7. Dec 1, 2003 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I really have to object to this. When we say that 0.999.... is 1, we are not talking about "measurement" and we are not talking about approximations.

    0.99999.... is not close to 1 it is 1: exactly equal to 1. As I said in another post, 0.99999... is defined as the limit of the sequence 0.9, 0.99, 0.999, ... and it is easy to show that that limit is 1.0.
     
  8. Dec 2, 2003 #7
    When 1.000... and 0.999... are two representations of the same number then:

    1.00... = 0.999...

    0.100... = 0.0999...

    0.0100... = 0.00999...

    0.00100... = 0.000999...

    0.000100... = 0.0000999...

    0.0000100... = 0.00000999...

    Therefore we can write:

    0.100... + 0.0100... = 0.0999... + 0.00999...

    0.0100... + 0.00100... = 0.00999... + 0.000999...

    But this is not true because:

    0.1100... not= 0.0999... + 0.00999... = 0.10999...8

    0.01100... not= 0.00999... + 0.000999... = 0.010999...8

    and so on ...


    Digit 8 is not the last digit but the limit digit or the unreachable digit of 0.999...

    Therefore 1.000... is not the limit of 0.999...
     
    Last edited: Dec 2, 2003
  9. Dec 2, 2003 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I sincerly hope that that was your idea of a joke.
     
  10. Dec 2, 2003 #9
    Check out the other thread with the identical post to convince yourself that it wasn't a joke... :frown:
     
  11. Dec 2, 2003 #10

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [moderator hat]

    This thread should be locked, since it just parallels the other one.

    [/moderator hat]

    - Warren
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Question about infinity
Loading...