Is 1.999...8 really equal to 2?

  • Context: Undergrad 
  • Thread starter Thread starter Blahness
  • Start date Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
3 replies · 2K views
Blahness
Messages
113
Reaction score
0
Elaborate.
Plus, wouldn't that mean 1.999...8 = 2?
 

Discussion

Physics news on Phys.org
God! Again this question. :cry:
 
Blahness said:
Elaborate.
Plus, wouldn't that mean 1.999...8 = 2?
By definition of a "base 10 numeration system", 0.999... means the limit of the sequence 0.9, 0.99, 0.999, 0.9999, ...
Those are the partial sums of a geometric series (a+ ar+ ar2+ ...) with a= 0.9 and r= 0.1. It's easy to show that a geometric series converges to a/(1-r) which in this case is 0.9/(1- 0.1)= 0.9/0.9= 1.
For the second question, what do you mean by "1.999...8"? If that ... indicates an infinite string then there is no end to put the 8 on! If you mean the limit of the sequence 1.8, 1.98, 1.998, 1.9998, ... (that's what 1.999... means- without the 8 of course) then it is equal to 2, yes.