1 = 0.999.....?
2011-10-19 22:15
Amuro
1 = 0.999.....?
http://zh.wikipedia.org/wiki/0.999%E2%80%A6#.E4.BB.A3.E6.95.B0
嚙誹梧蕭嚙踝蕭嚙踝蕭嚙踝蕭
2011-10-19 22:17
bread1997
嚙踝蕭嚙踝蕭嚙踝蕭嚙瘩?= =
2011-10-19 22:19
Amuro
1=1
0.999...=0.999...
1嚙盤嚙緻=嚙踝蕭L嚙踝蕭, 1=1
2011-10-19 22:21
bread1997
嚙稷嚙稻 #3 Amuro 嚙踝蕭嚙踝蕭嚙締
嚙瞑嚙踝蕭P嚙緞嚙瑾嚙踝蕭
2011-10-19 22:22
Amuro
嚙稷嚙稻 #4 bread1997 嚙踝蕭嚙踝蕭嚙締
嚙踝蕭P嚙緞嚙磐嚙踝蕭P嚙緞, 嚙盤嚙瘡嚙豌過嚙踝蕭P嚙緞 = 嚙踝蕭嚙踝蕭@嚙諉潘蕭
嚙賭撚嚙踝蕭@嚙誼呢?
2011-10-19 22:25
bread1997
嚙稷嚙稻 #5 Amuro 嚙踝蕭嚙踝蕭嚙締
嚙複學橘蕭嚙踝蕭嚙瑾嚙諉最梧蕭嚙踏的迎蕭嚙踝蕭�就嚙緻,0.9999999999999999............嚙穀嚙稼嚙踝蕭嚙踝蕭⑼嚙踝蕭嚙踝蕭|嚙磐1,嚙稽嚙踝蕭嚙誹伐蕭嚙盤嚙踝蕭,嚙瞑嚙誼塚蕭P嚙緞嚙緘嚙踝蕭嚙踝蕭,嚙穀嚙瘢嚙踝蕭嚙磐嚙瑾嚙諉蛛蕭嚙踝蕭嚙踝蕭,嚙踝蕭嚙磐嚙踝蕭嚙箠嚙瘡嚙諸堆蕭嚙踝蕭
2011-10-19 22:30
嚙踝蕭嚙瑾嚙踝蕭
嚙緻嚙諉被嚙瞋嚙論很久嚙瘤(嚙碼嚙諉世嚙踝蕭)
嚙談是覺嚙緻嚙踝蕭嚙踝蕭嚙諉伐蕭嚙磕嚙踝蕭嚙踝蕭嚙踝蕭
嚙踝蕭0.99999....嚙踝蕭嚙踝蕭嚙踝蕭1嚙踝蕭嚙誶可嚙瘡嚙踝蕭嚙踝蕭
2011-10-19 22:40
Amuro
嚙稷嚙稻 #7 嚙踝蕭嚙瑾嚙踝蕭 嚙踝蕭嚙踝蕭嚙締
嚙線嚙緯嚙踝蕭"嚙踝蕭"嚙瞇嚙緻, 0.9嚙踝蕭嚙踝蕭嚙踝蕭1嚙踝蕭嚙瞑嚙誼合嚙緲
嚙緯嚙豬莎蕭嚙皚嚙窮嚙踝蕭Y, 0.999... 嚙賦面嚙踝蕭嚙盤嚙踝蕭嚙踝蕭9, 嚙踝蕭嚙瞇嚙賤有嚙盤嚙踝蕭嚙踝蕭9, 嚙穀嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭1
嚙穀嚙線嚙磐嚙盤嚙踝蕭嚙踝蕭嚙踝蕭"1"嚙瞌嚙諉潘蕭, 嚙踝蕭嚙衛鳴蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭1
嚙踝蕭嚙盤 嚙穀嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙磐嚙踝蕭嚙確
(
0.999...
= 0.111.... * 9
= 1/9 * 9
= 1 )
嚙箠嚙踝蕭`嚙踝蕭嚙緘嚙複哨蕭concept嚙踝蕭嚙踝蕭嚙瞇嚙磐嚙踝蕭
2011-10-19 22:42
嚙踝蕭嚙瑾嚙踝蕭
嚙稷嚙稻 #8 Amuro 嚙踝蕭嚙踝蕭嚙締
嚙踝蕭嚙踝蕭0.111111111嚙踝蕭嚙諉就嚙瞌嚙踝蕭嚙踝蕭嚙踝蕭1/9
2011-10-19 22:52
WisH嚙踝蕭嚙瘤
嚙盤嚙瞌嚙踝蕭嚙瞌嚙諍數係嚙盤嚙緯嚙踝蕭
嚙瞇嚙磐嚙踝蕭嚙課謂迎蕭1嚙箠嚙踝蕭u嚙磐嚙篌嚙踝蕭嚙踝蕭
嚙踝蕭嚙瘤嚙瘩嚙踝蕭嚙踝蕭, 嚙瞇嚙碼嚙緹嚙瞌嚙踝蕭嚙複了
(嚙踝蕭嚙諉無嚙踝蕭嚙窮)
2011-10-19 23:04
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]WisH嚙踝蕭嚙瘤[/i] 嚙踝蕭 2011-10-19 10:52 PM 嚙緻嚙踝蕭
嚙盤嚙瞌嚙踝蕭嚙瞌嚙諍數係嚙盤嚙緯嚙踝蕭 [/quote]
嚙踝蕭嚙諍佗蕭 d 嚙瞎 in (嚙踝蕭
[quote]嚙趣帖嚙踝蕭 [i]WisH嚙踝蕭嚙瘤[/i] 嚙踝蕭 2011-10-19 10:52 PM 嚙緻嚙踝蕭
嚙踝蕭嚙瘤嚙瘩嚙踝蕭嚙踝蕭, 嚙瞇嚙碼嚙緹嚙瞌嚙踝蕭嚙複了[/quote]
___嚙瘡嚙窯...
[[i] 嚙踝蕭嚙踝蕭嚙諒恬蕭嚙� UniCorn 嚙踝蕭 2011-10-19 23:09 嚙編嚙踝蕭 [/i]]
2011-10-19 23:07
issac999
[quote]嚙趣帖嚙踝蕭 [i]WisH嚙踝蕭嚙瘤[/i] 嚙踝蕭 2011-10-19 22:52 嚙緻嚙踝蕭
嚙盤嚙瞌嚙踝蕭嚙瞌嚙諍數係嚙盤嚙緯嚙踝蕭
嚙瞇嚙磐嚙踝蕭嚙課謂迎蕭1嚙箠嚙踝蕭u嚙磐嚙篌嚙踝蕭嚙踝蕭
嚙踝蕭嚙瘤嚙瘩嚙踝蕭[color=Red]嚙踝蕭嚙稼/color], 嚙瞇嚙碼嚙緹嚙瞌嚙踝蕭嚙複了
(嚙踝蕭嚙諉無嚙踝蕭嚙窮) [/quote]
[quote]嚙趣帖嚙踝蕭 [i]UniCorn[/i] 嚙踝蕭 2011-10-19 23:04 嚙緻嚙踝蕭
嚙踝蕭嚙諍佗蕭 d 嚙瞎 in (嚙踝蕭
[color=Red]___[/color]嚙瘡嚙窯... [/quote]
2011-10-19 23:11
WisH嚙踝蕭嚙瘤
d嚙瞌d嚙踝蕭嚙磐嚙篇嚙踝蕭嚙踝蕭嚙諄塚蕭
(嚙踝蕭嚙瘡嚙磕嚙踝蕭嚙盤嚙緯嚙踝蕭嚙踝蕭嚙踝蕭嚙磐嚙緯嚙踝蕭, 嚙緹嚙線嚙瞋嚙踝蕭)
2011-10-19 23:25
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]WisH嚙踝蕭嚙瘤[/i] 嚙踝蕭 2011-10-19 11:11 PM 嚙緻嚙踝蕭
d嚙瞌d嚙踝蕭嚙磐嚙篇嚙踝蕭嚙踝蕭嚙諄塚蕭
(嚙踝蕭嚙瘡嚙磕嚙踝蕭嚙盤嚙緯嚙踝蕭嚙踝蕭嚙踝蕭嚙磐嚙緯嚙踝蕭, 嚙緹嚙線嚙瞋嚙踝蕭) [/quote]
嚙踝蕭嚙瞌 differentiation 嚙瞑 integration 嚙踝蕭簡嚙踝蕭...
嚙篇嚙踝蕭嚙諄迎蕭嚙瞌 d/dx 嚙瞑 嚙踝蕭dx
嚙盤嚙緯嚙踝蕭 = differentiation and integration
2011-10-19 23:31
WisH嚙踝蕭嚙瘤
ic
嚙踝蕭嚙緘嚙複殷蕭, 嚙踝蕭嚙瞌嚙緯嚙諉別嚙踝蕭0.999999嚙瞑1.1111嚙諉計嚙踝蕭嚙踝蕭????
2011-10-19 23:43
Amuro
嚙窯嚙踝蕭嚙緘嚙複可嚙踝蕭Y嚙踝蕭
嚙瘡嚙誹所迎蕭 嚙賭中嚙瑾嚙諍循嚙踝蕭嚙緘嚙複大嚙踝蕭嚙磐0.XXXXX... 嚙盤嚙踝蕭嚙踝蕭X
#9嚙踝蕭嚙踝蕭0.111... 嚙複對蕭W[color=Orange]嚙篌嚙踝蕭嚙踝蕭嚙踝蕭[/color]1/9
嚙踝蕭嚙諒家嚙踝蕭嚙踝蕭嚙篁嚙複人嚙踝蕭嚙瞇嚙穀嚙緲嚙諸佗蕭 0.111... [color=Lime]嚙踝蕭嚙踝蕭[/color] 1/9
[url=http://en.wikipedia.org/wiki/Repeating_decimal]http://en.wikipedia.org/wiki/Repeating_decimal[/url]
0.111...嚙賦面嚙踝蕭嚙碼嚙篁嚙踝蕭1? 嚙盤嚙踝蕭嚙緩嚙踝蕭嚙踝蕭?
嚙緘嚙瘦"1"嚙皚嚙複量嚙踝蕭嚙踝蕭,嚙踝蕭嚙穀嚙線嚙磐嚙瑾嚙諉小嚙踝蕭,嚙踝蕭嚙踝蕭嚙踝蕭嚙踝蕭嚙�1/9
嚙緘嚙瘦嚙踝蕭嚙盤嚙踝蕭嚙踝蕭1
0.11111111111111111111111111111111111...(嚙磊嚙踝蕭嚙盤嚙踝蕭嚙緝)
嚙瞌嚙諉數係嚙罷嚙線嚙磐嚙踝蕭嚙踝蕭1/9?
嚙緩嚙磐嚙蝓綽蕭L嚙踝蕭嚙踝蕭嚙踝蕭1/9?
嚙踝蕭嚙瘡嚙踝蕭嚙緯嚙踝蕭嚙編嚙盤嚙踝蕭嚙磐嚙璀嚙踝蕭嚙複喉蕭嚙踝蕭嚙踝蕭
嚙瞇嚙緲嚙論建立起嚙瑾嚙誼伐蕭嚙踝蕭嚙皚嚙踝蕭嚙磕, 嚙踝蕭嚙盤嚙箠嚙賞岩嚙瞌?
嚙誹哨蕭嚙踝蕭
2011-10-19 23:49
WisH嚙踝蕭嚙瘤
嚙瑾嚙瘡嚙瞎嚙踝蕭
嚙請解蛛蕭
2011-10-19 23:51
Amuro
嚙稷嚙稻 #17 WisH嚙踝蕭嚙瘤 嚙踝蕭嚙踝蕭嚙締
嚙緯prove "嚙盤嚙踝蕭"嚙踝蕭嚙磐嚙踝蕭嚙踝蕭
2011-10-20 00:35
paul22247
嚙璀嚙碾嚙磐嚙諍迎蕭嚙窮嚙踝蕭,嚙篇嚙盤嚙踝蕭x s嚙皚嚙褕塚蕭,嚙璀嚙賣左嚙瑾嚙箭,嚙璀嚙篇嚙盤x/2 s嚙皚嚙褕塚蕭,嚙璀嚙踝蕭I嚙諸低嚙瘦嚙箭嚙瑾嚙箭嚙皚嚙瑾嚙箭,嚙稽嚙踝蕭嚙瞌d嚙瑾嚙箭嚙磐嚙踝蕭嚙盤嚙踝蕭嚙豎多嚙踝蕭,嚙璀嚙衛鳴蕭嚙踝蕭嚙踝蕭嚙箠嚙踝蕭h嚙踝蕭嚙踝蕭嚙窮嚙踝蕭!
嚙踝蕭嚙瘦嚙璀嚙踝蕭嚙踝蕭嚙踝蕭r?嚙踝蕭嚙窮r ma嚙諒仔
嚙盤嚙踝蕭嚙豎多嚙踝蕭+嚙瘢嚙箠嚙瘡=嚙踝蕭嚙踝蕭嚙皚嚙複架
嚙踝蕭嚙踝蕭maths嚙踝蕭嚙緯嚙磐嚙踝蕭嚙碾嚙踝蕭
嚙瑾嚙踝蕭嚙踝蕭嚙瘡嚙課伐蕭1/10+1/10^2+1/10^3.......+1/10^n 嚙盤嚙踝蕭嚙豎多嚙踝蕭嚙皚嚙瞎=1/9
0.1111111111....嚙篌嚙踝蕭=1/9
嚙璀嚙瞇嚙線嚙磐on999999999
2011-10-20 11:42
UniCorn
[quote]嚙趣帖嚙踝蕭 [i]Amuro[/i] 嚙踝蕭 2011-10-19 11:43 PM 嚙緻嚙踝蕭
嚙窯嚙踝蕭嚙緘嚙複可嚙踝蕭Y嚙踝蕭
嚙瘡嚙誹所迎蕭 嚙賭中嚙瑾嚙諍循嚙踝蕭嚙緘嚙複大嚙踝蕭嚙磐0.XXXXX... 嚙盤嚙踝蕭嚙踝蕭X
#9嚙踝蕭嚙踝蕭0.111... 嚙複對蕭W嚙篌嚙踝蕭嚙踝蕭嚙踝蕭1/9
嚙踝蕭嚙諒家嚙踝蕭嚙踝蕭嚙篁嚙複人嚙踝蕭嚙瞇嚙穀嚙緲嚙諸佗蕭 0.111... 嚙踝蕭嚙踝蕭 1/9
[url]http://en.wikipedia.org/wiki/Repeating_dec[/url] ... [/quote]
0.1111111111....嚙磐=1/9,嚙諛己嚙踝蕭 long division 嚙瘠嚙瘠嚙踝蕭
0.9999999...=1 嚙踝蕭嚙諉是嚙稽嚙踝蕭嚙踝蕭怚u嚙緣嚙瑾嚙諉無嚙踝蕭嚙誰迎蕭嚙複吧...
嚙諸於不迎蕭嚙盤嚙踝蕭嚙瞌嚙篁嚙踝蕭,嚙課以嚙踝蕭嚙稽嚙緣嚙稿嚙誰得嚙踝蕭嚙瘡嚙盤嚙踝蕭
e.g.嚙踝蕭嚙諸師嚙踝蕭1嚙緘嚙褕後收嚙踝蕭嚙踝蕭,嚙璀嚙踝蕭嚙誰定嚙瞌嚙箭嚙踝蕭3600s 嚙褕佗蕭嚙踝蕭?
嚙諉歹蕭嚙瞌3600.00000...1s 嚙踝蕭 3599.999999...s ?
嚙緻嚙稽嚙瞌嚙稽嚙踝蕭嚙緣嚙稿嚙誰得嚙踝蕭嚙瘡嚙盤嚙踝蕭
(嚙瘡嚙磕嚙線嚙瞌嚙誹迎蕭嚙緲嚙踝蕭
2011-10-20 20:24
Amuro
[quote]嚙趣帖嚙踝蕭 [i]paul22247[/i] 嚙踝蕭 2011-10-20 00:35 嚙緻嚙踝蕭
嚙璀嚙碾嚙磐嚙諍迎蕭嚙窮嚙踝蕭,嚙篇嚙盤嚙踝蕭x s嚙皚嚙褕塚蕭,嚙璀嚙賣左嚙瑾嚙箭,嚙璀嚙篇嚙盤x/2 s嚙皚嚙褕塚蕭,嚙璀嚙踝蕭I嚙諸低嚙瘦嚙箭嚙瑾嚙箭嚙皚嚙瑾嚙箭,嚙稽嚙踝蕭嚙瞌d嚙瑾嚙箭嚙磐嚙踝蕭嚙盤嚙踝蕭嚙豎多嚙踝蕭,嚙璀嚙衛鳴蕭嚙踝蕭嚙踝蕭嚙箠嚙踝蕭h嚙踝蕭嚙踝蕭嚙窮嚙踝蕭!
嚙踝蕭嚙瘦嚙璀嚙踝蕭嚙踝蕭嚙踝蕭r?嚙踝蕭嚙窮r ma嚙諒仔
嚙盤嚙踝蕭嚙豎多嚙踝蕭+嚙瘢嚙箠嚙瘡=嚙踝蕭嚙踝蕭嚙皚 ... [/quote]
x嚙踝蕭嚙踝蕭@嚙箭, 2x嚙踝蕭嚙罷嚙踝蕭{嚙踝蕭嚙緬嚙踝蕭
嚙諄一嚙箭嚙瑾嚙箭嚙瑾嚙箭嚙豎計嚙皚嚙踝蕭
x + x/2 + x/2^2 + x/2^3 + x/2^4 +......+ x/2^n
嚙緘嚙瘦嚙璀嚙磐嚙緯嚙瑾嚙箭嚙瑾嚙箭嚙豎行的嚙確嚙磐嚙豎要嚙盤嚙踝蕭嚙褕塚蕭嚙踝蕭嚙篁嚙踝蕭Y嚙窮
嚙璀嚙踝蕭J嚙踝蕭嚙緹嚙盤嚙踝蕭嚙磐嚙線, 嚙踝蕭嚙瞎嚙踝蕭嚙稻嚙踝蕭嚙踝蕭堛嚙踝蕭a嚙踝蕭嚙踝蕭嚙踝蕭嚙緯嚙盤嚙踝蕭嚙褕塚蕭嚙踝蕭嚙箠嚙瘡嚙踝蕭F
嚙踝蕭graph嚙踝蕭嚙踝蕭嚙瘤嚙瞇嚙磐嚙踝蕭 http://en.wikipedia.org/wiki/Asymptote
嚙瘢嚙諸伐蕭Y嚙篁嚙踝蕭Y嚙窮?嚙稽嚙踝蕭嚙趣左1 - 0.999...嚙踝蕭,嚙稿嚙踝蕭嚙皚嚙複值好嚙踝蕭嚙磐limit嚙踝蕭嚙踝蕭嚙璀嚙踝蕭,嚙窯嚙踝蕭嚙磐嚙諒梧蕭嚙踝蕭0嚙皚嚙踝蕭,嚙諉所需時塚蕭嚙磐x/2^?嚙踝蕭
嚙踝蕭嚙踝蕭J嚙緘嚙踝蕭閬∴蕭P嚙踝蕭嚙踝蕭嚙誹伐蕭嚙褒過, 嚙踝蕭 嚙瑾嚙諉最短嚙皚嚙稿嚙踝蕭嚙踝蕭unknown嚙皚嚙褕塚蕭嚙踝蕭 嚙磐嚙踝蕭嚙箠嚙踝蕭嚙緻嚙踝蕭
嚙窯嚙踝蕭嚙誹永鳴蕭嚙線嚙罵嚙緹嚙踝蕭1 = 1 嚙踝蕭嚙踝蕭嚙踝蕭嚙盤嚙踝蕭
嚙瞑嚙瘢嚙璀嚙踝蕭嚙踝蕭嚙豎激嚙踝蕭?
2011-10-20 20:25
bread1997
嚙稷嚙稻 #19 paul22247 嚙踝蕭嚙踝蕭嚙締
嚙踝蕭蚢侉嚙�?:)
2011-10-20 21:40
paul22247
嚙豎你嚙磐嚙緯嚙踝蕭嚙踝蕭嚙踝蕭嚙瘡嚙瞇嚙瘡嚙箠嚙瘡嚙踝蕭嚙豌你
嚙踝蕭嚙瘦嚙篆
2011-10-20 21:51
Amuro
嚙稷嚙稻 #23 paul22247 嚙踝蕭嚙踝蕭嚙締
嚙踝蕭嚙踝蕭嚙諄堆蕭嚙諛哨蕭嚙瞇嚙踝蕭嚙踝蕭嚙瘦嚙篆
嚙踝蕭嚙瘦嚙篆嚙踝蕭嚙踝蕭N嚙踝蕭j嚙踝蕭嚙磐嚙諛想嚙諄自稱自己嚙踝蕭嚙磅嚙踝蕭嚙踝蕭O, 嚙諄者係嚙瑾嚙誕地嚙緙嚙皚嚙稷嚙踝蕭
嚙磅嚙諄者改蕭MK 嚙瘡嚙踝蕭嚙諛己嚙諉樣堆蕭嚙箱嚙瞇嚙緯嚙踝蕭
嚙磅嚙諄者改蕭嚙踝蕭x嚙磐嚙諍歹蕭嚙� 嚙踝蕭嚙踝蕭嚙諛己嚙踝蕭嚙踝蕭嚙磐嚙緯嚙踝蕭
嚙瘡嚙磕嚙諸瘀蕭wiki
....嚙踝蕭 嚙緯嚙踝蕭嚙踝蕭 嚙罵嚙赭成嚙踝蕭嚙皚嚙踝蕭嚙�
嚙踩有伐蕭嚙談你嚙瞇嚙磋d
[[i] 嚙踝蕭嚙踝蕭嚙諒恬蕭嚙� Amuro 嚙踝蕭 2011-10-20 21:52 嚙編嚙踝蕭 [/i]]
2011-10-20 21:56
嚙瞇嚙瞌嚙緘嚙踝蕭
嚙稷嚙稻 #24 Amuro 嚙踝蕭嚙踝蕭嚙締
嚙誹看你嚙誶歹蕭嚙瞎嚙踝蕭嚙踝蕭嚙瘦嚙篆嚙踝蕭嚙踝蕭嚙踝蕭嚙瞇嚙踝蕭嚙緲zz
2011-10-20 21:57
Amuro
嚙稷嚙稻 #25 嚙瞇嚙瞌嚙緘嚙踝蕭 嚙踝蕭嚙踝蕭嚙締
Explain please
2011-10-20 22:00
嚙瞇嚙瞌嚙緘嚙踝蕭
嚙稷嚙稻 #26 Amuro 嚙踝蕭嚙踝蕭嚙締
[url]http://wiki.komica.org/wiki3/?%E4%B8%AD%E4%BA%8C%E7%97%85[/url]
嚙踝蕭嚙璀嚙踝蕭嚙緻嚙諉字嚙踝蕭嚙緩嚙緬嚙踝蕭s嚙踝蕭
嚙緯嚙誹賂蕭嚙踝蕭嚙碼嚙諉迎蕭嚙豌我想嚙踝蕭嚙瘢嚙綞嚙踝蕭
嚙誶是嚙緯嚙篁嚙諛己嚙篁嚙踝蕭|嚙窮 (嚙踝蕭