#1
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¶Ù¡ËÃ×ͼԴ
$2.9\cdots$ (Êͧ¨Ø´à¡éÒà¡éÒ«éÓ) à»ç¹¨Ó¹Ç¹µÃáÂзÕèà»ç¹¨Ó¹Ç¹àµçÁ
¨Ò¡â¨·Âì¢éÒ§µé¹¶Ù¡ËÃ×ͼԴ¤èÐ 12 ¾ÄȨԡÒ¹ 2014 16:40 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ gon à˵ؼÅ: http://www.mathcenter.net/forum/showthread.php?t=3627 |
#2
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¶Ù¡µéͧ¤ÃѺ Áѹà·èҡѺ 3
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#3
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áµè¡çÂѧ§§ÍÂÙè´ÕÇèÒ·ÓäÁ (Êͧ¨Ø´à¡éÒà¡éÒ«éÓ) ¨Ö§à·èҡѺ 3 Áѹá¤èã¡Åéà¤Õ§¡Ñº 3 ÁÒ¡æææà·èÒ¹Ñé¹äÁèãªèàËÃͤèÐ
«Ö觡ÒÃà»ÅÕ蹷ȹÔÂÁ«éÓà»ç¹àÈÉÊèǹÁѹà»ç¹á¤è¤èÒã¡Åéà¤Õ§ËÃ×Íà»ÅèÒ¤èÐ |
#4
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A=2.999999...
10A=29.99999... ¹ÓÊÁ¡ÒÃÁÒź¡Ñ¹ 9A=27 A=3 ·È¹ÔÂÁ«éÓ ¤×Í àÈÉÊèǹ¤ÃѺ äÁèãªè¤èÒ»ÃÐÁÒ³
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Hope is what makes us strong. It's why we are here. It is what we fight with when all else is lost. 13 ¾ÄȨԡÒ¹ 2014 19:20 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ FranceZii Siriseth |
#5
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à¢éÒã¨ÇÔ¸Õ¡ÒÃà»ÅÕ蹷ȹÔÂÁ«éÓà»ç¹àÈÉÊèǹ¢Í§¤Ø³ gon áÅФس FranceZii Siriseth ¹Ð¤Ð ¢Íº¤Ø³ÁÒ¡¤èÐ
áµè㹡óնéÒàÃÒà¢Õ¹à»ÃÕºà·Õº¨Ó¹Ç¹ 2.999999... = 3.0000000... Áѹ¨Ð¶Ù¡µéͧËÃ×ͤèÐ à¾ÃÒÐËÅÑ¡¡ÒÃà»ÃÕºà·Õº¨Ó¹Ç¹·Õèà»ç¹·È¹ÔÂÁµéͧ´ÙµÑÇàŢ˹éҨش·È¹ÔÂÁ¡è͹äÁèãªèËÃ×ͤèÐ «Öè§ 2 ÁÕ¤èÒ¹éÍ¡ÇèÒ 3 |
#6
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Âѧä§ËÃͤÃѺ áµè 2.999... Áѹà·èҡѺ 3 à»ÃÕºà·ÕºÂѧä§ËÃͤÃѺ à¾ÃÒÐàÃÒà¢Õ¹àª×èÍÁ´éÇÂà¤Ã×èͧà·èҡѺä»áÅéÇ
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Hope is what makes us strong. It's why we are here. It is what we fight with when all else is lost. |
#7
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ÍéÒ§ÍÔ§:
ÍÂèÒ§µÒÁÃÙ» ÊÁÁµÔÇèÒÃÙ»ÊÕèàËÅÕèÂÁ¨ÑµØÃÑÊ¢¹Ò´ 1x1 = 1 µÒÃҧ˹èÇ ¨Ò¡¹Ñé¹¼Ááºè§¾×é¹·ÕèÍÍ¡à»ç¹ÊͧÊèǹ ´éÇÂÍѵÃÒÊèǹ 9:1 àÊÁÍ ¨Ðä´é¾×é¹·Õè«éÒÂÁ×ͤ×Í $\frac{9}{10}$ ¢Í§ 1 µÒÃҧ˹èÇ = $\frac{9}{10} \times 1 = \frac{9}{10}$µÒÃҧ˹èÇ áÅÐä´é¾×é¹·Õè $ x + y = 1 - \frac{9}{10} = \frac{1}{10}$ µÒÃҧ˹èÇ ¨Ò¡¹Ñé¹áºè§¾×é¹·ÕèÃÙ»ÊÕèàËÅÕèÂÁÁØÁ©Ò¡ $x+y = \frac{1}{10}$ µÒÃҧ˹èÇ ÍÍ¡à»ç¹ 2 ÊèǹẺà´ÔÁ¤×Í 9:1 ¹Ñ蹡ç¤×Í ¨Ðä´é $y = \frac{9}{10}$ ¢Í§ $x + y = \frac{9}{10}\times \frac{1}{10} = \frac{9}{100}$ áÅéÇ $x = (x+y) - y = \frac{1}{10} - \frac{9}{100} = \frac{1}{100}$ ¨Ò¡ÃÙ» àÃÒàËç¹ä´éªÑ´à¨¹ÇèÒ ¾×é¹·Õè·Ñé§ËÁ´¤×Í 1 µÒÃҧ˹èÇ ÂèÍÁà·èҡѺ¾×é¹·ÕèÃÙ»ÊÕèàËÅÕèÂÁÁØÁ©Ò¡´éÒ¹ã¹ÃÇÁ¡Ñ¹á¹è æ à»ç¹ÍÂèÒ§Í×è¹ä»äÁèä´é ¹Ñ蹡ç¤×Í $1 = \frac{9}{10} + y + x = \frac{9}{10} + \frac{9}{100} + x$ ÊÓËÃѺ $x$ ¡çáºè§ã¹·Ó¹Í§à´ÕÂǡѹàÃ×èÍÂä» ¡ç¨Ðä´é $x = \frac{9}{1000} + \frac{9}{10000} + \frac{9}{100000} + ...$ ¹Ñ蹤×Í $1 = \frac{9}{10} + \frac{9}{100} + \frac{9}{1000} + \frac{9}{10000} + \frac{9}{100000} + ... = 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + ... = 0.99999...$ ¶Ö§áÁéÇèÒÁѹ´Ùá»Å¡ æ ÇèÒ·ÓäÁ 1 ËÃ×Í 1.000... = 0.99999... áµèÂѧä§Áѹ¡çµéͧà»ç¹¨ÃÔ§ à¾ÃÒÐÇèÒ¾×é¹·ÕèãËèÊØ´¡çµéͧà·èҡѺ¾×é¹·ÕèÂèÍÂÃÇÁ¡Ñ¹ |
#8
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¢Íº¤Ø³ÁÒ¡¤èÐ ¤Ø³ gon ·ÕèªèÇÂ͸ԺÒÂÍÂèÒ§ÅÐàÍÕ´áÅк͡µÍ¹·éÒÂÇèÒÁѹ´Ùá»Å¡ æ áµèÂѧä§Áѹ¡çµéͧà·èҡѹ(â´¹ã¨ÁÒ¡)
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