Transcript
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KF = KH = FH hbf KF‗ = KH‗ = F‗H‗KO KI OI KO‗ KI‗ O‗I‗
KF = KF‗ KH = KH‗KO KO‗ KI KI‗
∃KHH‗ = ∃KII‗
II‗ ++ HH‗
II‗ = KI = KOHH‗ KH KF
II‗ = HH‗ T KOKF
Udi~i KO gs vdi mhebgcgohvgkb chovk~"KF
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_v~hgedv Agbi Miodhbgsms
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• Eibi~hvgkb kc sv~hgedv agbi mkvgkb ysgbe agbjhei
miodhbgsms dhs hauhws niib h okmmkb ~ixyg~imibv
gb mhodgbi fisgeb p~hovgoi"
• Havdkyed ithov sv~hgedv agbi ohbbkv ni eibi~hvif ysgbe
sgmpai miodhbgsms vdkyed skmi sgmpai miodhbgsms
h~i fisgebif syod vdhv vdiw ohb p~kfyoi hpp~ktgmhvi
sv~hgedv agbis ck~ sdk~v ~hbei kc mkvgkb"
• Vdisi hpp~ktgmhvi sv~hgedv agbi miodhbgsms dhs
gmpk~vhbv hppagohvgkbs gb mhodgbi fisgeb"
• Vdisi miodhbgsms ui~i ysif itvibsgiaw gb oahssgohamhodgbis syod hs svihm ibegbis"
• Pi~ciov sv~hgedv agbis ohb hask ni eibi~hvif ysgbe
agbjhei miodhbgsms nyv vdksi h~i ~iahvgiaw okmpait
miodhbgsms"
• Vdi~i h~i vuk oahssis kc sv~hgedv agbi miodhbgsms<
h' Hpp~ktgmhvi _v~hgedv Agbi Miodhbgsms"
n' Ithov _v~hgedv Agbi Miodhbgsms"
• Vdi sv~hgedv agbi miodhbgsms ui~i mksvaw fiiakpif gb
gbfysv~gha ~ikayvgkb fhws udib mhbw mhodgbis
~ixyg~if sv~hgedv agbi phvds gb vdig~ kpi~hvgkbs! udivdi~
gv uhs eygfgbe vdi pgsvkb kc ibegbis k~ ck~ kpi~hvgbe
hais"
• _v~hgedv agbi miodhbgsms ui~i fiiakpif nw
okbvgbykys icck~v gb v~hga hbf i~~k~ p~koiss ugvd mhjgbe
gbviaageibv h~ghvgkbs gb agbjhei miodhbgsms"
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_v~hgedv agbi mkvgkb miodhbgsms_v~hgedv agbi mkvgkb miodhbgsms h~i miodhbgsms! dhgbeh pkgbv vdhv mkis hakbe h sv~hgedv agbi! k~ bih~aw hakbe hsv~hgedv agbi! ugvdkyv nigbe eygfif nw h pahbi sy~choi
Oahssgcgohvgkb kc _v~hgedv agbi miodhbgsm
• Vdi sv~hgedv agbi miodhbgsms ui~i mksvaw fiiakpif gb
gbfysv~gha ~ikayvgkb fhws udib mhbw mhodgbis
~ixyg~if sv~hgedv agbi phvds gb vdig~ kpi~hvgkbs! udivdi~
gv uhs eygfgbe vdi pgsvkb kc ibegbis k~ ck~ kpi~hvgbe
hais"
• _v~hgedv agbi miodhbgsms ui~i fiiakpif nw
okbvgbykys icck~v gb v~hga hbf i~~k~ p~koiss ugvd mhjgbe
gbviaageibv h~ghvgkbs gb agbjhei miodhbgsms"
_v~hgedv agbi
miodhbgsmsHpp~ktgmhvi _v~hgedv Agbi
Miodhbgsms
Ithov _v~hgedv Agbi
Miodhbgsms
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"
Okbfgvgkb ck~ ithov sv~hgedv agbi mkvgkb<Gc pkgbv N mkis kb vdi og~oymci~iboi kc h og~oai ugvdoibvi~ K hbf ~hfgys KH! vdib! pkgbv O! udgod gs hbitvibsgkb kc HN v~hois h sv~hgedv agbi pi~pibfgoyah~ vk HK!p~kgfif p~kfyov kc HN hbf HO gs okbsvhbv"
Akoys kc pv"O ugaa ni hsv~hgedv agbi! ┶ vk HI gc! HNt HO gs okbsvhbvP~kkc<
∃HIO = ∃HNF
∶ HF = HNHO HI
∶ HI = HN T HOHF
Nyv HF= okbsvhbv
HI =okbsvhbv gc HN T HO =okbsvhbv"
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Pihyoiaagi~ ithov sv~hgedv agbi mkvgkbmiodhbgsm<
Pihyoiaagi~ ithov sv~hgedv agbi mkvgkb miodhbgsm
• Di~i! HI gs vdi gbpyv agbj hbf pkgbv I mkis hakbe hog~oyah~ phvd kc ~hfgys HI = HN"
• Hask! IO = IF = PO = PF hbf NO = NF"• Pkgbv P kc vdi miodhbgsm mkis hakbe ithov sv~hgedv
agbi pi~pibfgoyah~ vk NH itvibfif"
Vk p~ki N! I hbf P agi kb shmi sv~hgedv agbi<
• V~ghbeais NOF! IOF hbf POF h~i haa gsksoiaisv~ghbeais dhgbe okmmkb nhsi OF hbf hpit pkgbvsnigbe N! I hbf P"
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• Vdi~ick~i pkgbvs N! I hbf P hauhws agi kb vdipi~pibfgoyah~ ngsiovk~ kc OF"
• Diboi vdisi vd~ii pkgbvs hauhws agi kb vdi shmisv~hgedv agbi"
Vk p~ki p~kfyov kc NI hbf NP gs okbsvhbv"• Gb v~ghbeais NCO hbf PCO!
∶ NO> = CN> * CO> hbf PO> = PC > * CO>
∶ NO> - PO> = CN> - PC > = $CN * PC'T$CN - PC'= NP T NI
• Nyv sgboi NO hbf PO h~i okbsvhbvs! p~kfyov kc NP hbfNI gs okbsvhbv! udgod gs vdi okbfgvgkb ck~ ithovsv~hgedv agbi mkvgkb"
• Vdys pkgbv P hauhws mkis hakbe h sv~hgedv agbipi~pibfgoyah~ vk NH hs sdkub gb vdi cgey~i"
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5" Gc vdi hnki okbsgfi~hvgkbs h~i shvgscgif! vdib P ugaa mkihakbe h sv~hgedv agbi pi~pibfgoyah~ vk IK p~kfyoif"
P~kkc Lkgb NF" Okbsgfi~ ∃ HNF
HI = HX
HN HF
Vdgs okbfgvgkb gs egib"
C~km vdgs ui ohb sdku vdhv ∃HIX hbf ∃ HNF h~i sgmgah~
hbf diboi IX gs ph~haaia vk NF"
Okbsgfi~ ∃HNO
OP = HX = HI
ON HF HN
C~km vdgs nw h sgmgah~ h~eymibv gv ohb ni siib vdhv ∃HNO
hbf ∃ INP h~i sgmgah~ hbf diboi IP gs ph~haaia vk HO"
IX = HI
NF IN
IX = HI t NF
IN
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Ui ohb sdku ihsgaw vdhv ∃NPI hbf ∃ NHO h~i sgmgah~
IP = NI
HO NH
IP = NI t HO
NH
Ugvd K hs oibvi~ hbf ~hfgys KX f~hu h og~oai" Gv gbvi~siovIK p~kfyoif hvX‗" Lkgb XX‗"
Okbsgfi~ ∃ IXX‗ hbf ∃IPP‗"gv okyaf ni ihsgaw p~kif vdhvvdiw h~i sgmgah~"
IX = IX‗
IP‗ IP
IX‗"IP‗ = IX"IP
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Ui dhi ha~ihfw p~kif vdhv
IX = HI t NF
IN
IP = NI t HO
NH
IX‗"IP‗= HI t NF NI T HOIN NH
IX‗"IP‗= $NF"HO'"$HI"NI'HN>
IP‗= $NF"HO'"$HI"NI'HN>" IX‗
Lkgb NF hbf OC pi~pibfgoyah~ vk NF c~km O
NF = NC *CF hbf HO=NC - CF
IP‗= $NC*CF'$NC-CF'" $ HI"NI'
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HN>" IX‗
IP‗= $NC > -CF > '" $HI"NI ' HN>" IX‗
Nyv NC> = NO>-OC> hbf CF> =OF>-OC>
IP‗= $NO > -OC > '-$OF > -OC > '" $HI"NI ' HN>" IX‗
IP‗= $NO > - OF > '" $HI"NI ' HN>" IX‗
Gv okyaf ni siib vdhv HI! NI !HN!IX‗!NO hbf OF h~iokbsvhbv"
IP‗= okbsvhbv"
Vdhv gs fgsvhboi kc vdi ckkv kc vdi pi~pibfgoyah~ c~km Igs h okbsvhbv" Vdhv mihbs vdi pkgbv P ugaa hauhws mkihakbe h sv~hgedv agbi pi~pibfgoyah~ vk IK itvibfif"
Hpp~ktgmhvi sv~hgedv agbi mkvgkb miodhbgsm< H ciucky~ nh~ miodhbgsms ugvd oi~vhgb mkfgcgohvgkbs p~kgfihpp~ktgmhvi sv~hgedv agbi mkvgkbs"
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Sh~gkys hpp~ktgmhvi sv~hgedv agbi miodhbgsm8"Uhvvs‗s miodhbgsm">" Mkfgcgif _okvv-^yssiaa miodhbgsm"
?" E~hssdkppi~ miodhbgsm"6" Vodingodiccs miodhbgsm"9" ^kni~vs‗s miodhbgsm"
Uhvv miodhbgsm
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8"Uhvv miodhbgsm
Cgey~i sdkus UHVV miodhbgsm
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8" Gv gs h mkfgcgif o~kssif cky~ nh~ odhgb miodhbgsm
hbf uhs ysif nw UHVV"
>" 0NH08 gs h o~kssif cky~ nh~ odhgb gb udgod 0 hbf 08
h~i cgtif"
?" Gb vdi mihb pksgvgkb kc vdi miodhbgsm! vdi agbj 0N
hbf 08H h~i ph~haaia hbf vdi okypagbe ~kf HN gs
pi~pibfgoyah~ vk 08H hbf KN"
6" Vdi v~hogbe pkgbv P v~hois kyv hb hpp~ktgmhvi
sv~hgedv agbi ki~ vdi oi~vhgb pksgvgkb kc gvs mkimibvgc
PN = 08H
PH 0N
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P^KKC
8" H agvvai okbsgfi~hvgkb ugaa sdku vdhv gb vdi gbgvgha mihb
pksgvgkb kc vdi miodhbgsm! vdi gbsvhbvhbikys oibvi~
kc vdi agbj NH agis hv gbcgbgvw"
>" Vdi~ick~i vdi mkvgkb kc vdi pkgbv P gs hakbe vdi
i~vgoha agbi NH"
?" Aiv 0N‗H‗08 ni vdi biu pksgvgkb kc vdi miodhbgsm
hcvi~ vdi agbj KN hbf K8H h~i fgspahoif vd~kyed vdi
hbeai δ hbf σ ~ispiovgiaw"
6" Vdi gbsvhbviksys oibvi~ bku agis hv G"
h" _gboi vdi hbeai δ hbf σ h~i i~w smhaa!
vdi~ick~i
H~o NN‗ = H~o HH‗ k~ KN T δ = K8 T
∶ 0N = σ
‣‣‣‣‣‣‣‣‣‣‣‣‣‣‣$8'
08H δ
Hask H‗P‗ =GP‗ T σ hbf N‗P‗ =GP‗
Tδ
∶ H‗P = σ
‣‣‣‣‣‣‣‣‣‣‣‣‣‣‣$>'
N‗P‗ δ
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C~km ixyhvgkb $8' hbf $>'
0N = H‗P = HP k~ 08H = PN
08H N‗P‗ NP KN PH
Vdys vdi pkgbv P fggfis vdi agbj HN gbvk vuk ph~vs udksi
aibevd h~i gbi~siaw p~kpk~vgkbha vk vdi aibevd kc vdi
hflhoibv agbj"
>"Mkfgcgif _okvv-^yssiaa Miodhbgsm
8'Gv gs igfibv c~km vdi cgey~i vdhv vdgs miodhbgsm gsmhfi yp kc gsksoiais v~ghbeais: HN! HO hbf HK> h~i kc ixyha aibevds"
>'Vdgs miodhbgsm gs sgmgah~ vk vdi _okvv ^yssiamiodhbgsm nyv gb vdgs ohsi HN gs bkv ixyha vk HO hbf
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vdi pkgbv N hbf O h~i okbsv~hgbif vk mki gb dk~g|kbvhahbf i~vgoha fg~iovgkb"
?'H agvvai okbsgfi~hvgkb ugaa sdku vdhv gv ck~ms hb iaagpvgohav~hmmia! sk vdhv hbw pkgbv H kb NO v~hois hb iaagpsi
ugvd simg- mhlk~ HO hbf simg mhlk~ htgs HN"6' Gc vdi pkgbv H mkis gb h og~oai! vdib ck~ h pkgbv O vk
mki hakbe hb hpp~ktgmhvi sv~hgedv agbi! vdi aibevd KHmysv ni ixyha vk HN>+HO"
9'Vdgs gs agmgvif vk kbaw ck~ smhaa fgspahoimibv kc N"
?" E~hss dkppi~ miodhbgsm
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8" Vdgs miodhbgsm gs h mkfgcgohvgkb kc mkfgcgif _okvv^ysiia miodhbgsm ugvd fgcci~iboi vdhv vdi pkgbvfkis bkv sagfi hakbe h sv~hgedv agbi! nyv mkis gb hog~oyah~ h~o ugvd oibvi~ K"
>" Gv gs h cky~ nh~ miodhbgsm hbf haa phg~ h~i vy~bgbephg~s hs sdkub gb cgey~i"
?" Gb vdgs miodhbgsm! vdi oibvi~ K hbf K8 h~i cgtif"6" Vdi agbj KH ksogaahvis hnkyv K vd~kyed hbf hbeai
HKH8 udgod ohysis vdi pkgbv P vk mkis hakbe hog~oyah~ h~o ugvd K hs h oibvi~ hbf K8P hs ~hfgys"
9" Ck~ smhaa hbeyah~ fgspahoimibv kc KP kb ihod sgfi kc vdi dk~g|kbvha !vdi pkgbv X kb vdi itvibsgkb kc vdi
agbj PH v~hois kyv hb hpp~ktgmhviaw h sv~hgedv phvdXX‗ "
6"Vodingodiccs $Odinwodi' miodhbgsm
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9"Vodingodiccs $Odinwodi' miodhbgsm
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8'Gv gs h cky~ nh~ miodhbgsm gb udgod vdi o~kssif agbjKH hbf K8N h~i kc ixyha aibevd"
>' Vdi pkgbv P udgod gs vdi mgfpkgbv kc HN v~hois kyv hb
hpp~ktgmhviaw sv~hgedv agbi ph~haaia vk 008 "
?' Vdi p~kpk~vgkbs kc vdi agbj h~i ysyhaaw syod vdhv vdi
pkgbv P gs ithovaw hnki K k~ K8 gb vdi itv~imi
pksgvgkb kc vdi miodhbgsm" g"iudib vdi NH agis N08"
6' Gv mhw ni bkvif vdhv vdi pkgbv P ugaa agis kb h sv~hgedv
agbi ph~haaia vk 008 gb vdi vuk itv~imi pksgvgkbs hbf
gb vdi mgf pksgvgkb! gc vdi aibevd kc vdi agbj h~i gb
p~kpk~vgkbs
HN < 008 < KH = 8 < > < >"9
3" ^kni~v%s _v~hgedv Agbi Miodhbgsm
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^kni~v%s _v~hgedv Agbi Miodhbgsm
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8" Gv gs hask h cky~ nh~ odhgb miodhbgsm! udgod gb mihb
pksgvgkb dhs vdi ck~m kc h v~hpi|gym"
>" Vdi agbj KH hbf K8N h~i kc ixyha aibevd hbf KK8 gs
cgtif"
?" H nh~ PX gs ~gegfaw hvvhodif vk vdi agbj HN hv gvs
mgffai pkgbv P"
6" H agvvai okbsgfi~hvgkb ugaa sdku vdhv gc vdi miodhbgsm
gs fgspahoif hs sdkub nw vdi fkvvif agbis gb cgey~i!
vdi pkgbv X ugaa v~hoi kyv hb hpp~ktgmhviaw sv~hgedv
agbi"
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^kni~v‗s miodhbgsm
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8" Vdgs gs h cky~ nh~ miodhbgsm! udi~i! POF gs h sgbeaigbvie~ha agbj"
>" Hask! fgmibsgkbs HO! NF! OP hbf PF h~i haa ixyha"?" Pkgbv P kc vdi miodhbgsm mkis i~w bih~aw hakbe
agbi HN"
Gbvi~mgvvibv mkvgkb miodhbgsms
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• Hb gbvi~mgvvibv-mkvgkb miodhbgsm gs h agbjhei udgodokbi~vs okbvgbykys mkvgkb gbvk gbvi~mgvvibv mkvgkb"
• Vdisi miodhbgsms h~i okmmkbaw ysif ck~ gbfitgbe
gb mhodgbi vkkas"
Eibih udiia miodhbgsm
8' Gb vdi miodhbgsm sdkub gb cgey~i! agbj H gs f~gi~ hbfgv okbvhgbs h pgb udgod ibeheis ugvd vdi sakvs gb vdif~gib agbj N"
>' Vdi sakvs h~i pksgvgkbif gb syod h mhbbi~! vdhv vdipgb ibvi~s hbf aihis vdim vhbeibvghaaw hkgfgbe
gmphov akhfgbe fy~gbe v~hbsmgssgkb kc mkvgkb"?' Gb vdi miodhbgsm sdkub! vdi f~gib mimni~ mhjis
kbi-cky~vd kc h ~ikayvgkb ck~ ihod ~ikayvgkb kc vdif~gi~"
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6' Vdi akojgbe pahvi! udgod gs mkybvif kb vdi f~gi~!p~iibvs vdi f~gib mimni~ c~km ~kvhvgbe itoipvfy~gbe vdi gbfitgbe pi~gkf
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