- #1
Blahness
- 113
- 0
Elaborate.
Plus, wouldn't that mean 1.999...8 = 2?
Plus, wouldn't that mean 1.999...8 = 2?
Finding the Is 1.999...8 Really Equal to 2?
- Context: Undergrad
- Thread starter Blahness
- Start date
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Discussion Overview
The discussion revolves around the mathematical interpretation of the number represented as 1.999...8 and its relationship to the number 2. Participants explore the implications of this notation within the context of base 10 numeration systems and limits of sequences.
Discussion Character
- Debate/contested
Main Points Raised
- Some participants question whether 1.999...8 can be considered equal to 2, suggesting that the notation may imply different interpretations.
- One participant references the definition of 0.999... as the limit of a geometric series, arguing that it converges to 1, which may imply a similar reasoning for 1.999... leading to 2.
- Another participant challenges the meaning of "1.999...8," arguing that if the ellipsis indicates an infinite string, there cannot be a definitive end to place the 8.
- There is a suggestion that if 1.999...8 is interpreted as the limit of the sequence 1.8, 1.98, 1.998, 1.9998, then it could be equal to 2.
Areas of Agreement / Disagreement
Participants express differing views on the interpretation of 1.999...8, with no consensus reached on its equality to 2. The discussion remains unresolved regarding the implications of the notation.
Contextual Notes
There are limitations in the definitions and interpretations of the notation being discussed, particularly regarding the treatment of infinite sequences and the placement of the digit 8.
- #2
hypermorphism
- 504
- 1
No. See the Archives.
- #3
Lisa!
Gold Member
- 672
- 96
God! Again this question. 
- #4
HallsofIvy
Science Advisor
Homework Helper
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By definition of a "base 10 numeration system", 0.999... means the limit of the sequence 0.9, 0.99, 0.999, 0.9999, ...Blahness said:
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.
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