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#1
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ÅͧÍèÒ¹´Ù¤ÃѺ¤ÃѹèÒ¨ÐÁÕ»ÃÐ⪹ìºéÒ§
1. ·ÄÉ®Õ ( theorem ) ËÁÒ¶֧ á¹Ç¤Ô´ (¢éÍàʹÍ) ·Ò§¤³ÔµÈÒʵÃì·ÕèÊÒÁÒÃض¾ÔÊÙ¨¹ìä´éÇèÒà»ç¹¨ÃÔ§ àªè¹ ¶éÒàÃÒàʹÍÇèÒ "¶éÒ p ¤×ͨӹǹ੾ÒÐáÅÐ p | ab,áÅéÇ p | a ËÃ×Í p | b" áÅéÇàÃÒÊÒÁÒö¾ÔÊÙ¨¹ìä´éÇèÒà»ç¹¨ÃÔ§ ¹Ô¾¨¹ì´Ñ§¡ÅèÒÇ¡ç¨Ð¡ÅÒÂà»ç¹·ÄÉ®Õ ¤ÃѺ 2. ¡ÒäҴà´Ò ( conjecture ) ËÁÒ¶֧ á¹Ç¤Ô´ (¢éÍàʹÍ) ·Ò§¤³ÔµÈÒʵÃì·ÕèäÁèÃÙéÇèÒ¨ÃÔ§ËÃ×Íà·ç¨ ( truth value is unknown ) àªè¹ ¶éÒàÃÒàʹÍÇèÒ "¶éÒ p ¤×ͨӹǹ੾ÒÐáÅÐ p | ab,áÅéÇ p | a ËÃ×Í p | b" áÅéÇàÃÒÂѧäÁèä´é·Ó¡ÒþÔÊÙ¨¹ìä´éÇèÒà»ç¹¨ÃÔ§ËÃ×Íà·ç¨ ¹Ô¾¨¹ì´Ñ§¡ÅèÒÇ¡ç¨Ð¶×ÍÇèÒà»ç¹¡ÒäҴà´Ò¤ÃѺ 3. ¾ÔÊÙ¨¹ì ( proof ) ¤×Í¡ÒÃ͸ԺÒÂÇèÒ ·ÄɮչÑ鹨ÃÔ§ ä´éÍÂèÒ§äà àªè¹ àªè¹ ¶éÒàÃÒàʹÍÇèÒ "¶éÒ p ¤×ͨӹǹ੾ÒÐáÅÐ p | ab,áÅéÇ p | a ËÃ×Í p | b" ·Ó¡ÒþÔÊÙ¨¹ìä´é´Ñ§¹Õé ¾ÔÊÙ¨¹ì ¶éÒÊÁÁµÔãËé a äÁèÊÒÁÒöËÒôéÇ p ,à¾ÃÒеÑÇËÒà (divisor) ·Õèà»ç¹ºÇ¡¢Í§ p ÁÕ੾ÒÐ 1 áÅÐ p à·èÒ¹Ñé¹ , «Ö觺͡ä´éÇèÒ Ë.Ã.Á. ¢Í§ p áÅÐ a ¤×Í 1 ( gcd(p,a) = 1 ) ´Ñ§¹Ñé¹ â´ÂÍéÒ§ÍÔ§¨Ò¡ ¢éÍàʹÍá·Ã¡¢Í§ ÂÙ¤ÅÔ´ ( Euclid's lemma ) ¨Ðä´é p | b 4. ¢éÍàʹÍá·Ã¡ ( lemma ) ËÁÒ¶ԧ ·ÄÉ®ÕÍÂèÒ§§èÒ·Õè¾ÔÊÙ¨¹ì â´Âãªé·ÄÉ®ÕÍ×è¹æ àªè¹ ¨Ò¡ ·ÄÉ®Õ 1 "ãËé a áÅÐ b à»ç¹¨Ó¹Ç¹àµçÁ áÅÐäÁà»ç¹ 0 ÊÒÁÒöºÍ¡ä´éÇèÒà»ç¹ relatively prime àÁ×èÍ gcd(a,b) = 1" Euclid's lemma : ¶éÒ a | bc, ´éÇ gcd(a,b) = 1, áÅéÇ a | c proof àÃÒàÃÔèÁ¨Ò¡·ÄÉ®Õ 1 à¢Õ¹ã¹ÃÙ»¢Í§ linear combination ä´é 1 = ax + by àÁ×èÍ x áÅÐ y à»ç¹¨Ó¹Ç¹àµçÁ ¤Ù³ÊÁ¡ÒôéÇ c ¨Ðä´é c = 1c = (ax + by)c = acx + bcy à¾ÃÒÐÇèÒ a | ac áÅÐ a | bc, «Öè§à»ç¹ä»µÒÁ a | (acx + bcy) «Ö觨ѴÃÙ»ãËÁèä´é¤×Í a | c 5. ¼Å·ÕèµÒÁÁÒ ( corollary ) ËÁÒ¶֧ ÊÔ觷Õèä´éÁÒ¨Ò¡¡ÒþÔÊÙ¨¹ì·ÄÉ®Õ˹֧áÅéÇã¹ÃÐËÇèÒ§·ÕèàÃÒ¾ÔÊÙ¨¹ì·ÄɮչÑé¹àÃÒä´éÍÕ¡·ÄÉ®Õ˹Öè§Áҷѹ·Õ â´Â»¡µÔáÅéÇ corolary ¨Ðà¢Õ¹µèͨҡ·ÄÉ®Õ àÍÒá¤è¹Õé¡è͹¡çáÅéǡѹ áÅéǤÃÒÇ˹éÒ¼Á¨Ðà¢Õ¹à¾ÔèÁãËé¶éÒÁÕ¼Ùéʹ㨹ФÃѺ
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¡ÅѺÁÒáÅéǨéÒ |
#2
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ÍéÒ§ÍÔ§:
ÍéÒ§ÍÔ§:
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#3
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lemma à·èÒ·Õè¼ÁÃÙé¨Ñ¡ ¨Ð¾ÔÊÙ¨¹ìÁÒ¡è͹ main theorem áÅéǾͨоÔÊÙ¨¹ì main theorem ¨ÃÔ§æ ¡ç¨Ð¹Ó lemma ¹ÕéÁÒªèÇÂÍéÒ§ äÁèãªèàËÃͤÃѺ ËÃ×ͼÁ à¢éÒ㨼Դ
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à¡ÉÕ³µÑÇàͧ »ÅÒÂÁԶعÒ¹ 2557 áµè¨Ð¡ÅѺÁÒà»ç¹¤ÃÑ駤ÃÒÇ |
#4
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Âѧ¢Ò´ÍÂÙèÊÒÁÍÂèÒ§·ÕèÊÓ¤ÑÁÒ¡¤ÃѺ
¤Ó¹ÔÂÒÁ(definition) ¤Ó͹ÔÂÒÁ(undefined term) áÅÐ ÊѨ¾¨¹ì(axiom) ¹Í¡¨Ò¡¹Õé¡çÂѧÁÕ paradox theorem ºÒ§·Õ¡çàÃÕ¡ÇèÒ proposition ¤ÃѺ
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site:mathcenter.net ¤Ó¤é¹ 15 ¾ÄÉÀÒ¤Á 2005 07:28 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ nooonuii |
#5
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µÍº ¤Ø³ warut
1. ¤ÇÒÁËÁÒ¢ͧ lemma à»ç¹ÍÂèÒ§·Õè ¤Ø³ passer-by ºÍ¡ÅФÃѺ ¢Íâ·É·Õ¤ÃѺ lemma : a simple theorem used to prove other theorem. 2. Êèǹ ·ÄɮշÕè 1 à»ç¹·ÄɮդÃѺäÁèäªè¹ÔÂÒÁ ¤ÇÒÁËÁÒ (µèÍ) 6. ¹ÔÂÒÁ ( Definition ) ¤×Í¡ÒÃ͸ԺÒÂËÃ×ÍãËé¤ÇÒÁËÁÒµèÒ§æ ·Õè¨Ðãªéà¾×èÍãËéà¢éÒ㨤ç¡Ñ¹â´ÂÍÒÈÑ ¤Ó͸ԺÒ·ÕèàËÁÒÐÊÁ·ÕèÊØ´ àªè¹ ÊÕèàËÅÕèÂÁ´éÒ¹¢¹Ò¹¤×Í ÊÕèàËÅÕèÂÁ·ÕèÁÕ´éÒ¹µÃ§¢éÒÁ¢¹Ò¹¡Ñ¹ 7. ͹ÔÂÒÁ (Indefinition) ¤×ÍÊÔ觵èÒ§æ ·ÕèàÃÒäÁèÊÒÁÒöãËé¹ÔÂÒÁä´é àªè¹ àÊ鹵ç 8.ÊѨ¾¨¹ì (axiom) ¤×Í¢éͤÇÒÁ·Õ赡ŧ¡Ñ¹äÇéàº×éͧµé¹ ·Õè¨ÐµéͧÂÍÁÃѺâ´ÂäÁèµéͧ¾ÔÊÙ¨¹ì àªè¹ ÊÒÁÒöÅÒ¡àÊ鹵ç¼èÒ¹¨Ø´Êͧ¨Ø´ä´éà¾Õ§àÊé¹à´ÕÂÇà·èÒ¹Ñé¹ 9. ¹Ô¾¨¹ì (proprosition) (á»Å¶Ù¡ËÃ×Íà»ÅèÒ) ËÁÒ¶֧¢éͤÇÒÁ·ÕèÊÒÁÒöºÍ¡ä´éÇèÒ à»ç¹¨ÃÔ§ËÃ×Í à·ç¨ à·èÒ¹Ñé¹ ¨ÐäÁèÊÒÁÒöºÍ¡ÇèÒà»ç¹·Ñ駨ÃÔ§áÅÐà·ç¨ä´éã¹¢éͤÇÒÁà´ÕÂǡѹ àªè¹ âÅ¡¡ÅÁ (¨ÃÔ§), ËÁÙµé͹á¡Ðä´é (à·ç¨ à¹×èͧ¨Ò¡äÁèãªè babe )
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¡ÅѺÁÒáÅéǨéÒ |
#6
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à·èÒ·ÕèàÃÕ¹ÁÒ·ÄɮշÕè 1 ¹Õèà»ç¹¹ÔÂÒÁ¤ÃѺ àÅÂʧÊÑÂÇèÒ àÃҨйÔÂÒÁ¤ÓÇèÒ relatively prime ¡Ñ¹Âѧ䧴Õ
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site:mathcenter.net ¤Ó¤é¹ |
#7
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¤ÓÇèÒ Proprosition ¹ÕèµÃ§¡Ñº¤ÓÇèÒ »Ãо¨¹ì ¤ÃѺ
Êèǹ¤ÓÇèÒ ¹Ô¾¨¹ì ¹Õè ÃÙéÊÖ¡¨ÐµÃ§¡Ñº¤ÓÇèÒ Expression ¹Ð¤ÃѺ ÊѨ¾¨¹ì¹ÕèºÒ§·Õ ¡çãªé¤ÓÇèÒ Postulate ¤ÃѺ ( à¾ÔèÁãËéÍա˹èÍ ) »Å. àÃ×èͧâÅ¡¡ÅÁ ¹Õè¨ÃÔ§æ Áѹ¡çäÁèä´é¡ÅÁ¨ÃÔ§æ ÍèҹФÃѺ ºÒ§Êèǹ¡çäÁè¡ÅÁ¨¹ÍÍ¡à»ç¹Ç§ÃÕ仺éÒ§àËÁ×͹¡Ñ¹ àÅÂäÁè¤èÍÂá¹èã¨ÇèÒÁѹÊÒÁÒöºÍ¡ä´éÃÖ»èÒÇÇèÒà»ç¹¨ÃÔ§ËÃ×Íà·ç¨ÍèФÃѺ
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" ¨Ø´ÊÙ§ÊØ´ ¤×Í àº×éͧÅèÒ§·Õè¼èÒ¹ÁÒ ¨Ø´ÊÙ§¤èÒ ¤×Í ÊÔè§ã´Ë¹ÍªÕÇÕ " 16 ¾ÄÉÀÒ¤Á 2005 18:34 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ tana |
#8
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ãªèáÅéÇ à»ç¹¹ÔÂÒÁ¨ÃÔ§æ ´éÇ ¢Íº¤Ø³¤ÃѺ
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¡ÅѺÁÒáÅéǨéÒ |
#9
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theorem ¡Ñº proposition ᵡµèÒ§¡Ñ¹Âѧä§àËÃͤÃѺ ÁÕ¢éÍÊѧࡵ㹡ÒÃàÅ×Í¡ãªéËÃ×Íà»ÅèÒ?
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#10
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ÍéÒ§ÍÔ§:
Proposition ÍÒ¨¨Ðà»ç¹¤ÇÒÁ¨ÃÔ§àÅç¡æ·Õèä´éÁÒâ´ÂµÃ§¨Ò¡¹ÔÂÒÁ«Öè§àÃÒÍÒ¨¹ÓÁÒãªéã¹âÍ¡ÒʵèÍä» Theorem ¤×ͤÇÒÁ¨ÃÔ§·ÕèÍÒ¨¨Ðä´éÁÒ¨Ò¡¡Ãкǹ¡ÒþÔÊÙ¨¹ì·Õè«Ñº«é͹¢Öé¹ ÍÒ¨ÁÕ¡ÒÃÍéÒ§ÍÔ§¶Ö§¹ÔÂÒÁ ,lemma ËÃ×Í theorem ·Õèä´éÃѺ¡ÒþÔÊÙ¨¹ìäÇéáÅéÇ¡è͹˹éÒ¹Õé ».Å. ÍÂèÒàª×èͼÁÁÒ¡ ¼Á¡çÁÑèÇàÍÒàËÁ×͹¡Ñ¹
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site:mathcenter.net ¤Ó¤é¹ |
#11
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áËÁà«Õ¹áÁç·Âѧá¡äÁèÍÍ¡àÅ ¼Áà¢éÒ㨤ÃѺ à¾ÃÒÐàÃÒäÁèãªèªÒǵÐÇѹµ¡·Õè¡Ó˹´ ¹ÔÂÒÁµèÒ§æ ·Ò§¤³ÔµÈÒʵÃì áÅÐàÍÒà¢éÒ¨ÃÔ§æ ¡ÒÃãªé§Ò¹¡çÁÕ·Õèà¢éÒ㨵èÒ§¡Ñ¹á¡µÒÁÊѧ¤Á áÅÐÂÔè§ÊèǹÁÒ¡¨Ðà»ç¹¹Ñ¡ÍèÒ¹¡Ñ¹à»ç¹ÊèǹãËè àÃÕ¡ä´éÇèÒà»ç¹¼Ùéʹã¨à·èÒ¹Ñé¹ áµè¼Ùé·ÕèÁÕâÍ¡ÒÈ㹡ÒþѲ¹Ò¨ÃÔ§æ ÁÑ¡¨Ðà»ç¹¤¹·ÕèÁÕ°Ò¹ÐËÃ×ÍâÍ¡ÒÈ·Ò§Êѧ¤ÁÊÙ§ «Öè§ÁÕÁÒ¡ã¹Êѧ¤ÁµÐÇѹµ¡ ¤Ô´ÇèÒ¤§µéͧÍèҹ˹ѧÊ×Í੾ÒдéÒ¹àÃ×èͧ¡ÒÃà¢Õ¹º·¤ÇÒÁ(¤ÇÒÁàËç¹)·Ò§¤³ÔµÈÒʵÃì ¨Ö§¨ÐÁÕµÑÇÍÂèÒ§¡ÒÃãªéËÃ×ͤÓá¹Ð¹ÓÍ×è¹æ
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#12
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ÍéÒ§ÍÔ§:
Proposition à»ç¹·Äɮպ·àÅç¡æ·ÕèäÁèµéͧÍÍ¡áç¾ÔÊÙ¨¹ìÁÒ¡¹Ñ¡¤ÃѺ à»ç¹¤ÇÒÁ¨ÃÔ§¢Ñé¹¾×é¹°Ò¹·ÕèÊÒÁÒö¾ÔÊÙ¨¹ìä´é§èÒÂæ Theorem à»ç¹·Äɮպ··ÕèÁÕÕ¤ÇÒÁÊӤѡÇèÒ Proposition «Öè§ÍÒ¨¨Ðãªé¡Ãкǹ¡ÒþÔÊÙ¨¹ì·Õè«Ñº«é͹¡ÇèÒ
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site:mathcenter.net ¤Ó¤é¹ |
#13
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Åͧ¡µÑÇÍÂèÒ§ axiom ·Õè¡ÅÒÂà»ç¹ theory ä´éÁÑé¤ÃѺ
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site:mathcenter.net ¤Ó¤é¹ |
#14
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¶ÒÁ¡ÅѺ¶Ö§·ÕèÇèҫѺ«é͹ ¹Ñé¹à»ç¹Âѧ䧤ÃѺ ÊÓËÃѺ Êèǹ·ÕèÇèÒãªé¼Ô´ ¤§ËÒÂÒ¡ ÊÓËÃѺ¼Ùé·ÕèàÃÕ¹ÃÙéà»ç¹ËÅÑ¡ áµè¤§ËÒ¼Ùé·Õèãªé¼Ô´§èÒ ÊÓËÃѺ¼Ùé·Õè¤é¹¤ÇéÒÇÔ¨ÑÂ
áÅТ͵ͺ ÍÂèÒ§àªè¹ ¤ÇÒÁ¨ÃÔ§·Õè¾Ù´¡Ñ¹·ÑèÇä»ã¹Çѹ¹Õé Çѹ˹éÒ¡çÍÒ¨ÁÕ¼Ùé¾ÔÊÙ¨¹ìã¹á§èµèÒ§æ áÅÐËÒ¡ä´éÃѺ¡ÒÃÂÍÁÃѺÇèÒÁÕ»ÃÐâª¹ì ¡ç¡ÅÒÂà»ç¹·ÄÉ¯Õ µÑÇÍÂèÒ§·Õè¨Ð¡ÅèÒÇ ¤×Í Database theory ¹ÕèãËÁèæ àÅ «Öè§à»ç¹·ÄɯշÕè»ÃСͺ´éÇÂ˹èÍÂÂèÍÂÁÒ¡ÁÒ áÅÐÁÕ¡ÒûÃÐÂØ¡µìàÍÒ¤³ÔµÈÒʵÃì¼ÊÁà¡ÕèÂÇ¢éͧ´éÇ ´Ùä´é·Õè http://en.wikipedia.org/wiki/Database_theory |
#15
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ÍéÒ§ÍÔ§:
Axiom ¢Í§ Database Theory ¤×ÍÍÐääÃѺ ¼ÁÃÙé¨Ñ¡à¾×è͹ËÅÒ¤¹¡ÓÅѧàÃÕ¹·Ò§´éÒ¹ Information Theory Íѹ¹ÕéµèÒ§¨Ò¡ Database Theory Âѧ䧤ÃѺ
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site:mathcenter.net ¤Ó¤é¹ |
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