Lesson_4 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 4 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 4 lebxz crlb oxr :dkixr oxia xnr ,cwy inrp x"c ,ipinipa a`ei 'text :ddbd uixw di`n :dqtcd :zexcbd .mixtqn ly dveaw A `dz . M ≥ a ,a ∈ A lkly jk M ∈ R miiw m` lirln dneqg A .1 . A dveawl lirln mqg `xwii M . m ≤ a ,a ∈ A lkly jk m ∈ R miiw m` rxln dneqg A .2 . A dveawl rxln mqg `xwii m . | a | ≤ M a ∈ A lkly jk M miiw n"n` ,rxlne lirln dneqg A m` dneqg A .3 :`nbec lirln dneqg `l la` . e` ,lynl ,- 1 2 i"r rxln dneqg N = { 1 , 2 , 3 ,... } dveawd • .dneqg `l okle ,lynl , 17 i"r lirln) .dneqg (1 , 2] rhwd ,xnelk A = x ∈ R 1 < x ≤ 2 dveawd • ( . i"r rxlne . max A epnqp . dveawd ly meniqwnd `xwp `ed xzeia lecb xtqn yi A-a m` .4 . min A epnqp . dveawd ly menipind `xwp `ed xzeia ohw xtqn yi A-a m` .5 :`nbec . 1 / ∈ A ik menipin oi` A-l j` . max x ∈ A x = 2 A = (1 , 2] dveawa • :miiwny xtqn `ed A ly menxteqd .lirln dneqg A `dz .6 . A ly lirln mqg `ed .` . A ly xzeia ohwd lirln mqgd `ed .a sup A :epnqp :miiwny xtqn `ed A ly menitpi`d .rxln dneqg A `dz .7 . A ly rxln mqg `ed .` . A ly xzeia lecbd rxln mqgd `ed .a inf A :epnqp :`nbec-a hiap • . sup A = 2 ∈ A , inf A = 1 / ∈ A A = (1 , 2] :zexrd .dveawa xai` gxkda `l menitpi` /menxteqd .1 . sup A = max A f` sup A ∈ A m` .2m` ....
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This note was uploaded on 03/12/2011 for the course MATH 104010 taught by Professor Dr.miriambarazinna during the Winter '11 term at Technion.

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Lesson_4 - 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 4 lebxz...

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