[B! mathematics] ita-wasaã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

ita-wasa id:ita-wasa

mathematicsã«é–¢ã™ã‚‹ita-wasaã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (5)

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ã€Žãƒ—ãƒ©ã‚¤ãƒ ãƒŠãƒ³ãƒãƒ¼ã‚ºã€ - ä¸–ç•Œç·šèˆªè·¡è”µ
ã€Ž ãƒ—ãƒ©ã‚¤ãƒ ãƒŠãƒ³ãƒãƒ¼ã‚º ã€ã€é¢ç™½ã„ã‘ã©ã€é…·ã„æœ¬ã ã€‚ ç´ æ•°ã«ã¾ã¤ã‚ã‚‹æ´å²ã‚„äº‹å®Ÿã‚’æœ¬å½“ã«ãŸãã•ã‚“ãŸãã•ã‚“è©°ã‚åˆã‚ã›ã¦ã‚ã‚‹ã€‚ã ã‹ã‚‰ã€ç´ æ•°ã‚’æ„›ã™ã‚‹äººã§ã‚ã‚Œã°ã©ã®ãƒšãƒ¼ã‚¸ã‹ã‚‰ã§ã‚‚æ¥½ã—ãèªã‚€ã“ã¨ãŒã§ãã‚‹ã ã‚ã†ã€‚å°‘ãªãã¨ã‚‚ç§ã¯æ¥½ã—ã‹ã£ãŸã€‚ã§ã‚‚ã€ç¿»è¨³ãŒæ°—ã«ãªã£ãŸã€‚ The series 1/1 + 1/2 + 1/3 +. .. + 1/n diverges as n tends to infinity. ã“ã‚Œã®è¨³ãŒã“ã‚“ãªã«ãªã£ã¦ã„ã‚‹ã€‚ ç´šæ•° 1/1 + 1/2 + 1/3 + â€¦ + 1/nã¯ï¼Œnã‚’ç„¡é™å¤§ã«è¿‘ã¥ã‘ã‚‹ã¨åŽæŸã—ã¾ã™ã€‚ ã—ããƒ¼ã‚ˆã€‚ã‚ªã‚¤ãƒ©ãƒ¼å…ˆç”Ÿã€æ¶™ç›®ã€‚"diverges"ã£ã¦æ›¸ã„ã¦ã‚ã‚‹ã˜ã‚ƒã‚“ã€‚ã¨ã„ã†ã‹ã€ã‚‚ã®ãŒèª¿å’Œç´šæ•°ã ã‹ã‚‰ç§ã§ã‚‚è£œæ£ã§ããŸã‘ã‚Œã©ã‚‚ã€ç§ãŒçŸ¥ã‚‰ãªã„å®šç†ã‚„äºˆæƒ³ã‚‚ä¸€æ¯å‡ºã¦ããŸã®ã§ã€ãã†è¨€ã†ã®ã®ä¸ã«ã¯ç§ãŒæ°—ã¥ã„ã¦ã„ãªã„èª¤è¨³ã‚‚ã‚ã‚Šãã†ã ã€‚ ä»–ã«ã‚‚ã€Œã“ã‚‰ã€è¨³æ–‡ã®éƒ½åˆã§âˆ€ã¨âˆƒã®æŽ›ã‹ã‚‹é †åºã‚’å…¥ã‚Œæ›¿ãˆ
ita-wasa 2008/11/17
ã§ã‚‚ã€ç¿»è¨³ãŒæ°—ã«ãªã£ãŸã€‚ The series 1/1 + 1/2 + 1/3 +. .. + 1/n diverges as n tends to infinity. ã“ã‚Œã®è¨³ãŒã“ã‚“ãªã«ãªã£ã¦ã„ã‚‹ã€‚ ç´šæ•° 1/1 + 1/2 + 1/3 + â€¦ + 1/nã¯ï¼Œnã‚’ç„¡é™å¤§ã«è¿‘ã¥ã‘ã‚‹ã¨åŽæŸã—ã¾ã™ã€‚ ã“ã‚Œã¯ã²ã©ã„ã€‚

mathematics

neta
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ãƒŽãƒ¼ãƒ•ãƒªãƒ¼ãƒ©ãƒ³ãƒå®šç† - Wikipedia
ãƒŽãƒ¼ãƒ•ãƒªãƒ¼ãƒ©ãƒ³ãƒå®šç†ï¼ˆãƒŽãƒ¼ãƒ•ãƒªãƒ¼ãƒ©ãƒ³ãƒã¦ã„ã‚Šã€no-free-lunch theoremã€NFLï¼‰ã¯ã€ç‰©ç†å¦è€… David H. Wolpert ã¨ William G. Macready ãŒç”Ÿã¿å‡ºã—ãŸçµ„åˆã›æœ€é©åŒ–ã®é ˜åŸŸã®å®šç†ã§ã‚ã‚‹ã€‚ãã®å®šç¾©ã¯ä»¥ä¸‹ã®ã‚ˆã†ã«ãªã‚‹ã€‚ â€¦â€¦ã‚³ã‚¹ãƒˆé–¢æ•°ã®æ¥µå€¤ã‚’æŽ¢ç´¢ã™ã‚‹ã‚ã‚‰ã‚†ã‚‹ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã¯ã€å…¨ã¦ã®å¯èƒ½ãªã‚³ã‚¹ãƒˆé–¢æ•°ã«é©ç”¨ã—ãŸçµæžœã‚’å¹³å‡ã™ã‚‹ã¨åŒã˜æ€§èƒ½ã¨ãªã‚‹ â€”â€‰Wolpert and Macreadyã€1995å¹´ ã“ã®å®šç†ã®åç§°ã¯ã€ãƒã‚¤ãƒ³ãƒ©ã‚¤ãƒ³ã®SF å°èª¬ã€Žæœˆã¯ç„¡æ…ˆæ‚²ãªå¤œã®å¥³çŽ‹ã€ï¼ˆ1966å¹´ï¼‰ã§æœ‰åã«ãªã£ãŸæ ¼è¨€ã®"There ain't no such thing as a free lunch."ã«ç”±æ¥ã™ã‚‹ã€‚ã‹ã¤ã¦é…’å ´ã§ã€Œé£²ã¿ã«æ¥ãŸå®¢ã«ã¯æ˜¼é£Ÿã‚’ç„¡æ–™ã§æŒ¯ã‚‹èˆžã†ã€ã¨ã„ã†å®£ä¼ãŒè¡Œã‚ã‚ŒãŸãŒã€ã€Œç„¡æ–™ã®æ˜¼é£Ÿã€ã®ä»£é‡‘ã¯é…’ä»£ã«å«ã¾ã‚Œã¦ã„ã¦å®Ÿéš›ã«ã¯ã€Œç„¡æ–™ã®æ˜¼é£Ÿã€ãªã‚“ã¦ã‚‚ã®ã¯æœ‰ã‚‹è¨³ãŒãªã„
ita-wasa 2008/11/17
ã“ã®å®šç†ã¯ã€å•é¡Œé ˜åŸŸã«é–¢ã™ã‚‹çŸ¥è˜ã‚’ä½¿ã‚ãšã«éºä¼çš„ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã‚„ç„¼ããªã¾ã—æ³•ãªã©ã®æ±Žç”¨æŽ¢ç´¢ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã‚’ä½¿ã†ã“ã¨ã«åå¯¾ã™ã‚‹è«–æ‹ ã¨ã—ã¦ä½¿ã‚ã‚Œã‚‹ã€‚ä»–ã®æ±Žç”¨ã‚¢ãƒ«ã‚´ãƒªã‚ºãƒ ã«ã‚‚é©ç”¨ã•ã‚Œã¦ããŸãŒã€ä¸€èˆ¬ã«ãƒŽãƒ¼ãƒ•ãƒªãƒ¼ãƒ©

mathematics

methodology
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ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã®è¿‘ä¼¼ - Wikipedia
ã“ã®è¨˜äº‹ã«ã¯å‚è€ƒæ–‡çŒ®ã‚„å¤–éƒ¨ãƒªãƒ³ã‚¯ã®ä¸€è¦§ãŒå«ã¾ã‚Œã¦ã„ã¾ã™ãŒã€è„šæ³¨ã«ã‚ˆã£ã¦å‚ç…§ã•ã‚Œã¦ãŠã‚‰ãšã€æƒ…å ±æºãŒä¸æ˜Žçžã§ã™ã€‚ è„šæ³¨ã‚’å°Žå…¥ã—ã¦ã€è¨˜äº‹ã®ä¿¡é ¼æ€§å‘ä¸Šã«ã”å”åŠ›ãã ã•ã„ã€‚ï¼ˆ2015å¹´12æœˆï¼‰ log n! ã¨ n log n âˆ’ n ã¯ n â†’ âˆž ã®ã¨ãæ¼¸è¿‘ã™ã‚‹ ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã®è¿‘ä¼¼ï¼ˆè‹±: Stirling's approximationï¼‰ã¾ãŸã¯ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã®å…¬å¼ï¼ˆè‹±: Stirling's formulaï¼‰ã¯ã€éšŽä¹—ã€ã‚ã‚‹ã„ã¯ãã®æ‹¡å¼µã®ä¸€ã¤ã§ã‚ã‚‹ã‚¬ãƒ³ãƒžé–¢æ•°ã®æ¼¸è¿‘è¿‘ä¼¼ã§ã‚ã‚‹ã€‚åç§°ã¯æ•°å¦è€…ã‚¸ã‚§ã‚¤ãƒ ã‚ºãƒ»ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ï¼ˆè‹±èªžç‰ˆï¼‰ã«ã¡ãªã‚€ã€‚ ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã®è¿‘ä¼¼ã¯ç²¾åº¦ã«å¿œã˜ã¦ã„ãã¤ã‹ã®å½¢ãŒã‚ã‚‹ã€‚å¿œç”¨ä¸Šã‚ˆãä½¿ã‚ã‚Œã‚‹å½¢ã®å…¬å¼ã¯ã€ãƒ©ãƒ³ãƒ€ã‚¦ã®è¨˜å·ã‚’ç”¨ã„ã¦ã€ ã§ã‚ã‚‹ã€‚O(log n) ã«ãŠã‘ã‚‹æ¬¡ã®é …ã¯ (1/2)log 2Ï€n ã§ã‚ã‚‹ã€‚æ•…ã«ã€æ¬¡ã«ã‚ˆã„è¿‘ä¼¼ã®æ¼¸è¿‘å…¬å¼ï¼ˆè‹±èªžç‰ˆï¼‰ã¯ ã§ã‚ã‚‹[1]ã€‚ï¼ˆã“ã“ã§è¨˜å· ã¯ä¸¡è¾ºã®æ¯”ãŒï¼ˆn
ita-wasa 2008/11/01
ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã®è¿‘ä¼¼ï¼ˆè‹±: Stirling's approximationï¼‰ã¾ãŸã¯ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã®å…¬å¼ï¼ˆè‹±: Stirling's formulaï¼‰ã¯ã€ã‚¬ãƒ³ãƒžé–¢æ•°(æˆ–ã„ã¯éšŽä¹—)ã®æ¼¸è¿‘è¿‘ä¼¼ã§ã‚ã‚‹ã€‚æ•°å¦è€…ã‚¸ã‚§ã‚¤ãƒ ã‚ºãƒ»ã‚¹ã‚¿ãƒ¼ãƒªãƒ³ã‚°ã«å› ã‚€ã€‚ \Gamma(z+1)\approx\sqrt{2{\pi}z}\left(\frac{z}

mathematics
ãƒªãƒ³ã‚¯
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ita-wasa 2008/09/16
ã“ã†ã—ã¦ã‚²ãƒ¼ãƒ‡ãƒ«ã¯è¨€ã†ã€‚ã€Œæ•°å¦ã¯ã“ã®æ„å‘³ã§å®Œå…¨åŒ–ä¸å¯èƒ½ã§ã€ãã®æ˜Žè¨¼çš„å…¬ç†ã¯æœ‰é™ã®è¦å‰‡ã§å°½ãã•ã‚Œã‚‹ã“ã¨ã¯æ±ºã—ã¦ãªã„ã€‚ã™ãªã‚ã¡äººé–“ç²¾ç¥žã¯ï¼ˆç´”ç²‹æ•°å¦ã®é ˜åŸŸå†…éƒ¨ã«ãŠã„ã¦ã™ã‚‰ï¼‰ã„ã‹ãªã‚‹æœ‰é™ã®æ©Ÿæ¢°ã‚’ã‚‚ç„¡é™ã«è¶…è¶Šã—

mathematics
ãƒªãƒ³ã‚¯
Proof Explorer - Home Page - Metamath
The aleph null above is the symbol for the first infinite cardinal number, discovered by Georg Cantor in 1873 (see theorem aleph0). This is the starting page for the Metamath Proof Explorer subproject (set.mm database). See the main Metamath Home Page for an overview of Metamath and download links. If you wish to contribute your own proofs to the Metamath project, see How can I contribute to Metam
ita-wasa 2008/07/17
the Metamath Proof Explorer has over 8,000 completely worked out proofs in logic and set theory, interconnected with over a million hyperlinked cross-references.

mathematics

metamath
ãƒªãƒ³ã‚¯
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