- 1-800-天鵝肉 [2009/06]
- Looking for civilized translation into Chinese, after reading 潑婦是怎樣煉成的 [2009/06]
- I have nothing to say [2009/05]
- After dinner and I love you [2009/04]
- Kylelong asked me to write this. [2009/03]
- 鳥語 de Manifesto [2009/06]
- I will not shut up! [2009/03]
- My Bumpy Blog Career [2009/02]
- My first blog, second edition [2009/02]
- My First Blog [2009/02]
- Is 1 bigger than 0.999... ? [2009/03]
Is 1 bigger than 0.9999..... ? This question is as important as Goldbach Conjecture.
If 1 is bigger than 0.999..., then what is their difference? Is it 0.1, or 0.01, or 0.001, or 0.0001?
No. The difference between 1 and 0.999.... is smaller than all of these. Acutually the difference is smaller than any positive numbers. That is, 1 is not any bigger than 0.999... by any difference you can think of. Therefore, 1 is not any bigger than 0.999....
Since 1 is not smaller than 0.9999... either, 1 then equals 0.999....
That is not the direct prove that 1 equals 0.999... though, here is the prove.
Let 0.9999.…..= X (1)
Multiple both sides by 10: 9.9999.….= 10X (2)
(2) - (1): 9 = 9X
Hence X = 1
Therefore 0.99999.…… = 1
This is Mir Conjecture.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the permission of the copyright holder, who is Mir.
PS: I can not type Chinese but love to read Chinese, the only language I can really understand. So please, no English, if you do not have to.
- [02/23]My First Blog
- [02/24]My first blog, second edition
- [02/25]My Bumpy Blog Career
- [03/05] Is 1 bigger than 0.999... ?
- [03/25]I will not shut up!
- [03/26]Kylelong asked me to write this.
- [04/16]After dinner and I love you
- [05/27]I have nothing to say
- [06/01]1-800-天鵝肉
- [06/12]Looking for civilized translation into Chinese, after reading 潑婦是怎樣煉成的
- [06/18]鳥語 de Manifesto
發表評論 評論 (21 個評論)
- 回復 Mir
- marnifan: 0.9999999999999999..............................還是不等於 1.Do you belive my logic though?
I proved something which is obviously wrong. Pure skill.
- 回復 marnifan
- Mir: Do you belive my logic though?額， 咱邏輯不好, 沒懂.
I proved something which is obviously wrong. Pure skill.
- 回復 Mir
- marnifan: 額， 咱邏輯不好, 沒懂.I though my article is stright forward. My failure. No wonder, no body said anything.
- 回復 Mir
- marnifan: 額， 咱邏輯不好, 沒懂.You do not understand my logic, but understand my humor better than others. That is comforting. I do not understand why we can not really laugh off things.
- 回復 Mir
- rtc4rtc: 悖論。小數點後有無窮多個9，所以（2）-（1）的算式得出9=9X的結果已經錯了，所以最後的結果是錯的。所以0.99999...<>1This is a real bite.
Infinite does not equal infinite, does it?
- 回復 練精化氣AAA
- 回你這個帖 算是做了違背原則的一件事情 本來絕不在論壇來談科學
算了吧 就一回
１ 和 ０。９９９９。。。的比較 你的定義不清楚
如果 是在 有理數集合 １>０。９９９。。
如果是在實數集合 本來 １。０就可以表示為 ０。９+０。０９+０。００９+０。０００９+。。。。。
以上數列 的和最後是收斂 到 １。０的
具體證明 自己去看書
- 回復 Mir
- 練精化氣AAA: 回你這個帖 算是做了違背原則的一件事情 本來絕不在論壇來談科學You are right.
算了吧 就一回
１ 和 ０。９９９９。。。的比較 你的定義不清楚
如果 是在 有理數集合
It is simply the sum of infinite convergent geometric sequence.
It is not really a science paper here. I just want to make something interesting. You can do it again.
- 回復 rtc4rtc
- Mir: This is a real bite.問題出在：9.999...-0.999...不可能得出9的結果。
Infinite does not equal infinite, does it?
- 回復 Mir
- rtc4rtc: 問題出在：9.999...-0.999...不可能得出9的結果。That is right. It is deceving. Obviously, not to you.
Thanks.
- 回復 已夜
- 練精化氣AAA: 回你這個帖 算是做了違背原則的一件事情 本來絕不在論壇來談科學您老太厲害了！！！！！
算了吧 就一回
１ 和 ０。９９９９。。。的比較 你的定義不清楚
如果 是在 有理數集合
- 回復 老糊塗
- 因為
0.9999999.........=0.3333333................x3
0.3333333.........=1/3
所以
0.9999999.........=1/3 x 3 =1
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