1. Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
    Dismiss Notice

0.99~=1

Discussion in 'Mathematics and Physics' started by rumiam, Apr 17, 2007.

  1. bananasiong

    bananasiong New Member

    Joined:
    Mar 7, 2006
    Messages:
    1,893
    Likes:
    7
    Location:
    Malaysia
    So what's the answer for this?
    0.99...99 PLUS 0.00...09 numerator and 9 denomenator, so the answer is still 1.

    How about this:
    Code (text):

    c = 0.99...99
    10c = 9.99...90
    10c - c = 9.99...90 - 0.99...99
    c = 0.99..99
     
  2. Roff

    Roff Well-Known Member

    Joined:
    May 16, 2003
    Messages:
    7,757
    Likes:
    89
    Location:
    Idaho, USA
    I think you miss the point. The string of 9's is infinitely long. You can't multiply by 10 and have a 0 show up at the end. If you think this will happen, then you don't understand the concept of infinity (which, admittedly, is difficult to comprehend).
     
  3. bananasiong

    bananasiong New Member

    Joined:
    Mar 7, 2006
    Messages:
    1,893
    Likes:
    7
    Location:
    Malaysia
    You're right too. But sometimes this can be done by imaging it, but not writing it out.
    For example, does anyone know about Heaviside's rule of partial fraction? There is a step which is something like this:
    Code (text):

    2(infinity)/infinity = 2
     
    But this cannot be written on the paper, and my lecturer call this as 'illegal job' :D
     
  4. dave

    Dave New Member

    Joined:
    Jan 12, 1997
    Messages:
    -
    Likes:
    0


     
  5. 3iMaJ

    3iMaJ New Member

    Joined:
    Feb 20, 2007
    Messages:
    129
    Likes:
    2

    infinity/infinity is an indeterimant form, IE you can't say 2*inf/inf = 2. The rules dont work like that.
     
  6. bananasiong

    bananasiong New Member

    Joined:
    Mar 7, 2006
    Messages:
    1,893
    Likes:
    7
    Location:
    Malaysia
    Yes, you can't say 2*inf/inf = 2, but this is done when the Heaviside's rule of partial fraction is applied. Something like this:
    Code (text):

    A = lim(x-->inf)  [2x/x  +  (x+B)/x]
    A = 3 [b]edited[/b]
     
    Straight away as shown above, but the infinity over infinity cannot be written.
     
    Last edited: May 29, 2007
  7. 3iMaJ

    3iMaJ New Member

    Joined:
    Feb 20, 2007
    Messages:
    129
    Likes:
    2
    Thats completely different. You're thinking of l'Hospital's rule where you have an indeterimant form involving limits it goes as:

    if lim g(x)/f(x) is either 0/0 or inf/inf then the following applies

    lim g(x)/f(x) = lim g'(x)/f'(x) where g'(x) and f'(x) are the derivatives which is what you would apply in your problem for both sections.

    Applying to your problem:

    lim (x->inf) 2*x/x + (x+B)/x = inf/inf + inf/inf as above l'Hospital's rule applies so:
    d/dx of above = 2 + 1/1 = 3

    lim (x -> inf ) [2*x/x + (x+B)/x] = 3
     
  8. bananasiong

    bananasiong New Member

    Joined:
    Mar 7, 2006
    Messages:
    1,893
    Likes:
    7
    Location:
    Malaysia
    Yes, you're right, that is 3. I didn't notice that. Why you call that as hospital's rule?? :)

    So, do you think 0.99...99 =1?
     
  9. 3iMaJ

    3iMaJ New Member

    Joined:
    Feb 20, 2007
    Messages:
    129
    Likes:
    2
    Yep. I posted the proof above. I'll post it again here.
     

    Attached Files:

  10. HudzonHawk

    HudzonHawk New Member

    Joined:
    Apr 9, 2006
    Messages:
    36
    Likes:
    0
    Location:
    England, Reading.
    Wait, people are still arguing over the whole 0.99.. = 1 equation despite the fact that a 5 minute search on the Internet will show thousands of credible sources which prove that the equation is true?

    No offense to anyone, but do you guys also disprove that the Earth is round?
     
  11. Roff

    Roff Well-Known Member

    Joined:
    May 16, 2003
    Messages:
    7,757
    Likes:
    89
    Location:
    Idaho, USA
    I've been trying to get the naysayers to rewrite the Wikipedia entry. No takers yet. ;)
     
  12. bananasiong

    bananasiong New Member

    Joined:
    Mar 7, 2006
    Messages:
    1,893
    Likes:
    7
    Location:
    Malaysia
    So you can proof that 0.99...999 is not 1?
     
  13. Roff

    Roff Well-Known Member

    Joined:
    May 16, 2003
    Messages:
    7,757
    Likes:
    89
    Location:
    Idaho, USA
    No, my statement was meant as sarcasm. What I meant was, if the naysayers believe so strongly that 0.999... is not equal to one, they should correct the Wikipedia entry. In English, we have a saying: "Put your money where your mouth is". You probably know that saying, or have a similar one in your culture.
     
  14. Nigel Goodwin

    Nigel Goodwin Super Moderator Most Helpful Member

    Joined:
    Nov 17, 2003
    Messages:
    39,228
    Likes:
    641
    Location:
    Derbyshire, UK
    The most amazing thing about this entire thread is that I've not deleted or locked it yet! :D :D :D
     
  15. Sceadwian

    Sceadwian Banned

    Joined:
    Oct 27, 2006
    Messages:
    14,047
    Likes:
    141
    Location:
    Rochester, US
    Please Nigel! PLEASE!
     
  16. marplots

    marplots New Member

    Joined:
    Jun 10, 2007
    Messages:
    7
    Likes:
    0
    1 - .999... is zero. The reason for this is that between any two different rational or irrational numbers, there is an infinite number of other numbers. The only way that there can be no difference between two numbers is if they are, in fact, the same number.

    Hence, there is no number between 3 and 3, but an infinite number of them between 3.141414... and 3.1399999...

    Since, for the expression .999... and 1 there is no number 'between', they are, in fact, the same number. Any difference you come up with is an artifact of your calculator or truncation.
     
  17. neoandrewson

    neoandrewson New Member

    Joined:
    Jun 16, 2007
    Messages:
    62
    Likes:
    0
    its tends to... level of significance always matters in practical stuff... but in math, no idea where it leads to...
     
  18. sheng_james

    sheng_james New Member

    Joined:
    Jul 19, 2007
    Messages:
    30
    Likes:
    0
    Location:
    philippines
    huh..
    all i know always like the current gain of a common-base configuration of BJT transistor 0.9999...aproximately equal to 1
     
  19. mcs51mc

    mcs51mc New Member

    Joined:
    Feb 7, 2006
    Messages:
    343
    Likes:
    2
    Location:
    Belgium
    Here's another one
    Imagine an archer 16 meters away from a target.
    When the arrow leaves the bow it has 16 meters to go.
    When half the way is done, still 8 meters to go
    After another half is done, still 4 meters to go
    After another half is done, still 2 meters to go
    After another half is done, still 1 meters to go
    After another half is done, still 0.5 meters to go
    After another half is done, still 0.25 meters to go
    After another half is done, still 0.125 meters to go
    After another half is done, still 0.0625 meters to go
    After another half is done, still 0.03125 meters to go
    After another half is done, still 0.015625 meters to go
    After another half is done, still 0.0078125 meters to go

    When will it reach the target?
    Never ... ... :D :confused: :D
     
  20. Papabravo

    Papabravo Well-Known Member

    Joined:
    Mar 9, 2006
    Messages:
    2,889
    Likes:
    25
    Location:
    Michigan, USA (GMT-5)
    This is a variation of Zeno's paradox. It involved a runner in a race against a turtle with a modest head start. In the paradox the poor runner was doomed to lose the race.
     
  21. Robot builder 101

    Robot builder 101 Guest

    ONLINE
    Lol, feels like im awlays half way done with my projects, aka they never get finished.

    In the human mind, we can percieve the number 1 with objects. For example, we see a orange as 1 orange. Therefore, we can have the whole number one, with only the number one as long as the human mind can percieve objects as only the number one.

    Other words, we are usually use to seeing only 1 object, meaning we thinnk the number one means 1.00000000000, not when it is actually 0.9999999999999999999999999999. We only see 1 object, so we get use to 1. Imagine seeing 0.9999999999 of a peice of paper... It would appear as 1, so we get familarized with one, when we dont actually see that it could be 0.9999999999.
     
    Last edited by a moderator: Aug 1, 2007

Share This Page