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(1)Deux infinis cousus main Joel Merker. To cite this version: Joel Merker. Deux infinis cousus main. Revue de Synthèse, Springer Verlag/Lavoisier, 1999, 120, pp.no. 1, 165-174. �hal-00003415�. HAL Id: hal-00003415 https://hal.archives-ouvertes.fr/hal-00003415 Submitted on 29 Nov 2004. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(93) ‘*‚d€ z —€ ˜ 1m | ‰Š}!~ z ‹:€ž‚¬m´l ¢ £–z ‰ ˜ *€I‹:€b‡ ‰d€b~1‹ nÐmT‰d€b~ | mT‚d}!n zÅz m~ z ‹:‰Š^€b~ z ‰Š}D~S© +è ·#è ù:ï ì ‚Š€ z –~*‰ | —€ z Ÿ¡}!~1‹*m^€b~ | m‚Š€ z Q

(94)  4å ü WÞ©1‹*mT~ z ‚›mO~*}!*‡#€†‚ЂЀ |ˆ¢ b—€ }Dnˆ‰d€#‘1šœ€ z šœ}D~ zh| mT~ | € z ‹ €b‡:‰Š€†~*~*€b~ | ‹ €ä~*}!–‡#€mT*¨4Ï!¥ c €Å‚¬m ۀb° ^€fŸUmoš n }!~ ˜ *€#‘1‹ €bl–*‰ z ‚›mÅn+€b‚›m | ‰Š‡:‰ | {—€ nˆ€ zh| n+€b‰Š~ | €Þ‘ ‚›mO‡:‰ | € zˆz €ä‹ €ä‚›mO‚А*­‰$€b n+€l1€b | ¦ }!*€bnŒ‚Š€ nD}!° ‚d€^‹ƒµ*~*€I*~*‰ | O—€ ~1m | *n+€b‚Š‚d€žl1}!–nłŠ€ z ‡:‰ | € zˆz € z ‘r‹ƒ„*~ÚÏüŸ¡}D~1‹*m^€b~ | mT‚U¥

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(97) ‘ O ÿO€ zh| ‰Š~“‹fb—€ l1m zˆz m *‚Š€Þ¥ ï _ èˆð ìó–íTÅ ð iQô#ê ïSb÷è è ž`ÎQ¥ O­ã$‚

(98) ‚А–‰

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(100) O Ü € |ˆ| €Û—€ š ¢ €b‚Š‚d€ÎØ  z €Sn–b—€ ‡&€† ‚Š€I€ ° | nˆ€S*~*€S~*}D*‡#€b‚d‚Š€4—€ š ¢ €b‚d‚Š€S‹:€™DnQm~1‹ €Å–~*‰k&š†m | ‰d}!~ z ‰ŠI*‚ Ž | mT~†—€ €#‘:mT‚Š}Dn z•˜ *€ÿ‹*mT~ z ‚›m |ˆ¢ b—€ }Dnˆ‰d€{‹ €‚$ƒ„–~*‰k&š†m | ‰d}!~ûb—€ ‚Š€§š | n+}TŸUmT‰d *‚Š€Þ‘T‚Uƒ„*~*‰`&šbm | ‰Š}D~ z ƒ„}Dlb—€ nQm‰ | €b~ ‹:€b*¨ | €b^l z ‘#‚›mřDnQmb‡ ‰ | m | ‰Š}D~nˆ€ ¦ }D‰Š™!~“mT~ | íœó&êèˆõ ðëQô#ù§ó ‚Š€ z| n+}!‰ z mDš | ‰d}!~ z †—€ ‚Š€š | nˆ}DmT™D~—€ | ‰ ˜ –€ z ŸUm‰Š *‚d€ z ·$!» fΕ€ | Ÿ¡}!n | €­·ˆÏ•Îf–~*‰k †—€ € z ¥  m‰ z ‰Š‚

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(102) ‘*‚d€ z šœ}D~ 1n+m | ‰Š}!~ z €b¨ lb—€ nˆ‰d^€b~ | m‚Š€ z m |ˆ| €b~1‹ –€ z ~*€Sl1}!*n+nˆ}!~ | z €fn–—€ mT‚d‰ z €†n ˜ 

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(104) ¥ ” } |+| m‚Š€3n–—€ mT™D‰ | mTSŸUmT‰ |

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(106) ƒ„‰d‚€b~=‹ }D~*~*€#‘*‰d‚

(107) € zh| € æ€§š | ‰d‡#€b^€ ~ | l1} zˆz ‰d *‚Š€© O c ƒµ‰Š~ | n+}:‹ *‰Šn+€S‹ € z € z l1mDšœ€ z ‰Š~:1~*‰ z ‹ €S™¤b—€ }:‹•—€ z ‰ ˜ *€ z Ÿ¡nQm!š | mT‚d€ z ‘–šœ€b~ z b—€ € z ‹f—€ šœn+‰Šnˆ€‚Š€ z| nQm Ž ¦ €§š | }D‰Šnˆ€ z l*n+}! 1m *‚Š€ z ‹ € z l“mTn | ‰›šœ–‚Š€ z ¥ O c € | €b~–‰Šnš }!^l | €{m |ˆ¢ b—€ ´m | ‰ ˜ –€bO€b~ | ‹ € zf| nQmT~ z Ÿ¡}!n+m | ‰Š}D~ z ‹&ƒˆ—€ š ¢ €b‚d‚Š€#¥ O c €ÿ‹fœ—€ 1~*‰dnŒ‹ € z ‡ ‰ | € z+z € z ^} £ €b~*~*€ z « &‡#€bn z ‚$ƒÊmb‡DmT~ | ® %'&)(€ | « &‡#€bn z ‚$ƒÊmnˆn+‰$€b n+€O® %'&+*l“mTn –~¶l–nˆ}:šœ€ z+z  z ‹ €S^} £ €b~*~–‰ z m | ‰d}!~

(108) ‘#‚Š€ zˆ˜ *€b‚Š‚d€ z ‹:‰k椀b nˆ€†~ | €b~=‹ ‰Šn+€š | ‰d}!~^€ | ‡!m‚Š€b–nŒmT z }!‚А–€#¥ O c €^‚Љdnˆ€I‚›m~*}!~n–†—€ ‡#€bn z ‰Š *‰d‚Љ | #—€ ‘&š!ƒ„€ z(|hŽ m  Ž ‹ ‰Šn+€ž‚¬m¶ *n+‰ z *nˆ€‹:€^‚$ƒµ‰Š~:‡!mnˆ‰¬mT~1šœ€Ol“mTnOn–—€ ¹1€b¨:‰Š}!~ | €b^l1}!n+€b‚Š‚d€#‘#‹*m~ z ‚Š€ z —€ ˜ 1m | ‰Š}D~ z ‹ƒ+b—€ ‡#}!‚d | ‰d}!~

(109) ¥ O c ƒ„‰d~ | nˆ}:‹ *‰dnˆ€I*~*€I‡ ‰ | € z+z € , š }!^l*‚d€b¨:€^·$šDƒ„€ z(|hŽ m  Ž ‹ ‰Šn+ € ,/.0Îå‹fœ—€ 1~*‰d€žl“mT} n S€ , º Ò 1· %'&)(<ì2%'&+*$Îf€ | ã 3  ,±º Ò +· %'&)(546%'&+*hÎÐ¥ Ö O  m‰ z m zˆz ‰$‘:€b~^nˆ€†l*nˆÖ €b~“mT~ |f| }D | € z ‚Š€ z ™!nQm~1‹ € z ‚d‰Š™D~*€ z ‹:€{‚›mÅÚ§—€ šbmT~*‰ ˜ –€Œšœ‚›m zˆz ‰ ˜ –€ ¢ m Ž ­‰Š‚ | }!~*‰d€b~*~*€Þ‘œ‹:€f™¤†—€ ~b—€ nQm‚Љ z €bn | }! z ‚d€ z šœ}!~1š €bl |Qz mT–¨Å}! ¦ € |Qz ~*}!~I‹ ‰`æb—€ nˆ€b~ | ‰¬mT *‚d€ z m{ šœ}D~1‹ ‰ | ‰Š}D~ ‹:€‚d€b*nŸUmT‰Šn+€Sl*nˆ€b~“‹ nˆ€ä‹ € z ‡Dm‚Š€b*n z šœ}!­l*‚Š€b¨:€ z ¥ Ü ƒµ€ zh| ‚d€Sšbm z l1}!–n‚UƒÊm!š | ‰Š}D~

(110) ¥ O­á3~ 1~r‘‹ƒµ‰Š^l1} z €bn‚Š€Sl*n+‰Š~1š ‰Šl1€S‹ƒªm!š | ‰Š}!~ z(| m | ‰Š}D~*~1mT‰dnˆ€­mI  šœ€ |ˆ| €Sm!š | ‰Š}D~8šœ}D^l*‚d€b¨ €€ | ‹ € ‡#}D‰ŠnmTl*l1mnQm°³ | n+€Å~1m | *n+€b‚Š‚d€b^€b~ | ‚¬mŸ¡}!~1š | ‰Š}D~8‹ƒµ}!~1‹ €S€ | ‚Uƒ+—€ ˜ 1m | ‰Š}D~‹ € ý š ¢ n}Þ² ‹ ‰Š~–™!€bn†¥  m‚ ¢ €b–nˆ€b z €b^€b~ | ‘–šœ€O~

(111) ƒµ€ zh| l“m z ‹*mT~ z š €O‚ЉЇ:nˆ€ œ ˜ *€O‚Uƒ„}!~8l1€b | mDšbš&—€ ‹:€bnOm  šœ€ z Ÿ¡}!~1‹:€ Ž ­€b~ |Ðz m |ˆ¢ b—€ ´m | ‰ ˜ –€ z ‹:€{‚›mSÙ—€ šbm~*‰ ˜ *€ ˜ 1m~ | ‰ ˜ *€{m^} £ €b~O‹ €‚$ƒ„€ z l1mDšœ€ ŽU| €b^l z Ÿ¡nQmDš | m‚ n+€b‚›m | ‰`Ÿ–‹ €l¸} z ‰ | ‰Š}D~

(112) ‘D‹ƒ+—€ š ¢ €b‚d‚Š€€ | ‹ €^}D*‡#€b^€ ~ | ¥ c ƒªmTl*n†€  z ‚UƒÊm | €b–nb‘bš € |ˆ| €fm~1mT‚ £*z €•m *~ z €b~ z €†~I‹ ‰Š^€†~ z ‰d}!~ş¡nQmDš | m‚Š€´b—€ ™ÞmT‚d€Omä ‹ €b*¨&¥ Ü ƒ„€ zh|hŽ m  Ž ‹ ‰dnˆ€ ˜ *€‚d€ z3| nÐm ¦ €š | }!‰Šn+€ z ‡:‰Šn | *€b‚d‚Š€ zz ƒµ‰›‹ €†~ | ‰ Ž “€b~ | mŒ ‹ € z ™¤†—€ }:‹f—€ z ‰ ˜ –€ z ‹ €•‹ ‰d^€b~ z ‰Š}!~{Ÿ¡nÐm!š | mT‚Š€åb—€ ™ÞmT‚d€SmŒ ‹ €b*¨&¥á3~ 1~

(113) ‘Dšœ€ |+| €•mT~1m‚ £–z €Ÿ¡nQm!š | mT‚d€ z €bI *‚Š€•m{l1} zh| €bnˆ‰d}!n+‰« šbmDš ¢ b—€ €S® 1‹*m~ z ‚d€fŸ¡}!nˆ´mT‚Љ z ^€-‹ € z }!l†—€ nQm | €b*n z mT | } Ž m!‹ ¦ }!‰Š~ |Qz•z *n•‹ € z 74º

(114) 1 ‡98rxg bj ‘œ5Z *;:=<(À?>+¿À6Á?@9A À?>о+B;CEDGF7¾:ÀIHJLKMDG>;<N)APOPQSR+DG>1RUT=CVN?WÀI<J9RÀXCO ¾)NI<1QLN Y@V>ŠÀ6Á1¾[Z:¾JÁtÀ¿\DG]SD¿\Q6*. ^}

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