View Single Post
  #10   Spotlight this post!  
Unread 29-08-2010, 23:24
Molten's Avatar
Molten Molten is offline
Registered User
AKA: Jason
FRC #1766 (Temper Metal)
Team Role: Mentor
 
Join Date: Dec 2006
Rookie Year: 2006
Location: Indiana
Posts: 2,289
Molten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond reputeMolten has a reputation beyond repute
Re: 0.9 repeating = 1?

Quote:
Originally Posted by Ether View Post
The mathematical meaning of the repeating decimal .999... is a limit.

It is the limit of the sequence of partial sums of the infinite series 9/10 + 9/100 + 9/1000 + ...

The sequence of partial sums of the above series is equal to (1-1/10), (1-1/100), (1-1/1000), ... (1-1/10^n)


Using the definition of limit of a sequence:



It can be shown that the limit of the above sequence is "1".

Therefore, "1" and ".999..." mean exactly the same thing. They are two different ways of writing the same real number.



The limit of a series of partial sums is not equal to the actual sum at all. This is by definition of a limit. A limit is what the function must approach ever closer without ever reaching it. If it ever actual reaches it at any point, then it is not truly its limit.
__________________
"Curiosity. Not good for cats, great for scientists."- Numb3rs

"They can break your cookie, but... you'll always have your fortune."-T.W. Turtle, Cats Don't Dance

"Tell my tale to those who ask. Tell it truly - the ill deeds along with the good, and let me be judged accordingly. The rest... is silence."-Dinobot, Beast Wars

"Though the first step is the hardest and the last step ends the quest, the long steps in between are certainly the best."
–Gruffi Gummi, Disney's Adventures of the Gummi Bears
Reply With Quote