Go to Post we learned that's what happens when you start building without even thinking about weight. next year, we'll lighten everything BEFORE we mount it. - greencactus3 [more]
Home
Go Back   Chief Delphi > Other > Math and Science
CD-Media   CD-Spy  
portal register members calendar search Today's Posts Mark Forums Read FAQ rules

 
Reply
Thread Tools Rating: Thread Rating: 2 votes, 5.00 average. Display Modes
  #16   Spotlight this post!  
Unread 24-08-2010, 03:20
BornaE's Avatar
BornaE BornaE is offline
Registered User
FRC #0842 (Formerly 39)
Team Role: Engineer
 
Join Date: Jan 2007
Rookie Year: 2007
Location: Gilbert, Arizona
Posts: 359
BornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant futureBornaE has a brilliant future
Re: 0.9 repeating = 1?

Lets try it this way.


X=.99999...
Thus X*10=9.99999....
now 9X = X*10 - X = 9.999... - 0.999... = 9.000
9X = 9
X = 1

And proven.
__________________
-Borna Emami
Team 0x27
Reply With Quote
  #17   Spotlight this post!  
Unread 28-08-2010, 15:18
ExTexan's Avatar
ExTexan ExTexan is offline
Parent and Volunteer
AKA: Richard Singletary
FRC #0548
 
Join Date: Mar 2010
Rookie Year: 2008
Location: Northville, MI
Posts: 128
ExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant futureExTexan has a brilliant future
Re: 0.9 repeating = 1?

Following your logic of :

Quote:
X=.99999...
Thus X*10=9.99999....
now 9X = X*10 - X = 9.999... - 0.999... = 9.000
9X = 9
X = 1
if X=1 then 10X=10 and
9X=10-.999999......

I'm not sure anything was proven!
__________________
What we think, or what we know, or what we believe is, in the end, of little consequence. The only consequence is what we do.

2010 REFEREE: Kettering, Ann Arbor, Wayne State, Troy, MI Championship, Atlanta-Newton field, IGVC TARDEC, MARC and upcoming KETTERING Kickoff.
Reply With Quote
  #18   Spotlight this post!  
Unread 29-08-2010, 18:35
RoboDesigners's Avatar
RoboDesigners RoboDesigners is offline
Registered User
VRC #2190 (RoboDesigners)
Team Role: Leadership
 
Join Date: Jun 2010
Rookie Year: 2006
Location: Virginia
Posts: 361
RoboDesigners will become famous soon enoughRoboDesigners will become famous soon enough
Re: 0.9 repeating = 1?

I'm not quite sure if I completely understand this, but here's another look at it:

1/9 = 0.111...

9*1/9 = 9*0.111...

9/9 = 0.999...

1 = 0.999...
__________________
Visit my website! www.RoboDesigners.com

VRC Team #2190

Twitter: @RoboDesigners
Reply With Quote
  #19   Spotlight this post!  
Unread 29-08-2010, 19:05
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,028
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: 0.9 repeating = 1?

Quote:
Originally Posted by ExTexan View Post
I'm not sure anything was proven! :confused
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:

Quote:
A real number L is said to be the limit of the sequence Xn if and only if for every real number ε > 0, there exists a natural number N such that for every n > N we have | Xn−L | < ε.
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.




Last edited by Ether : 29-08-2010 at 19:29.
Reply With Quote
  #20   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
  #21   Spotlight this post!  
Unread 30-08-2010, 00:00
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,028
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: 0.9 repeating = 1?

Quote:
Originally Posted by Molten View Post
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.

The meaning of the expression .999... is the sum of the infinite series.

And the sum of the series is the limit of the sequence of partial sums of the series (assuming the limit exists).

The limit in this case exists and is 1, so .999... means 1. They are two different ways of writing the same real number.



Last edited by Ether : 30-08-2010 at 00:10.
Reply With Quote
  #22   Spotlight this post!  
Unread 30-08-2010, 00:43
Ether's Avatar
Ether Ether is offline
systems engineer (retired)
no team
 
Join Date: Nov 2009
Rookie Year: 1969
Location: US
Posts: 8,028
Ether has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond reputeEther has a reputation beyond repute
Re: 0.9 repeating = 1?

Quote:
Originally Posted by Chris is me View Post
The limit is a point that it will never pass.
This is not a good definition of limit.

For example, consider the function f(x)=sin(x)/x. As x approaches infinity, this function "passes" zero infinitely many times. But the limit exists and is zero.


~
Reply With Quote
  #23   Spotlight this post!  
Unread 30-08-2010, 01:04
Chris is me's Avatar
Chris is me Chris is me is offline
no bag, vex only, final destination
AKA: Pinecone
FRC #0228 (GUS Robotics); FRC #2170 (Titanium Tomahawks)
Team Role: Mentor
 
Join Date: Dec 2008
Rookie Year: 2006
Location: Glastonbury, CT
Posts: 7,612
Chris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond reputeChris is me has a reputation beyond repute
Send a message via AIM to Chris is me
Re: 0.9 repeating = 1?

Quote:
Originally Posted by Ether View Post
This is not a good definition of limit.

For example, consider the function f(x)=sin(x)/x. As x approaches infinity, this function "passes" zero infinitely many times. But the limit exists and is zero.


~
Yeah, what you said. I'll get rid of my post.
__________________
Mentor / Drive Coach: 228 (2016-?)
...2016 Waterbury SFs (with 3314, 3719), RIDE #2 Seed / Winners (with 1058, 6153), Carver QFs (with 503, 359, 4607)
Mentor / Consultant Person: 2170 (2017-?)
---
College Mentor: 2791 (2010-2015)
...2015 TVR Motorola Quality, FLR GM Industrial Design
...2014 FLR Motorola Quality / SFs (with 341, 4930)
...2013 BAE Motorola Quality, WPI Regional #1 Seed / Delphi Excellence in Engineering / Finalists (with 20, 3182)
...2012 BAE Imagery / Finalists (with 1519, 885), CT Xerox Creativity / SFs (with 2168, 118)
Student: 1714 (2009) - 2009 Minnesota 10,000 Lakes Regional Winners (with 2826, 2470)
2791 Build Season Photo Gallery - Look here for mechanism photos My Robotics Blog (Updated April 11 2014)
Reply With Quote
Reply


Thread Tools
Display Modes Rate This Thread
Rate This Thread:

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
Common Questions with Repeating Answers Tom McCurdy General Forum 1 20-01-2005 15:06
Repeating as regional champs jagman2882 General Forum 13 29-03-2004 12:34


All times are GMT -5. The time now is 12:12.

The Chief Delphi Forums are sponsored by Innovation First International, Inc.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © Chief Delphi