Resumão Dos Mestres

 

Nheoueths Euaírmnhs EGPTZGM^ ()  1 {6, 7, :, >, 0, ...} * 1 {7, :, >, 0, ..} MEPDMZH^ ()  1 {..., -:, -7, 6, 7, :, >, ...} * 1 {..., -:, -7, 7, :, >, ...} + 1 {6, 7, :, >, 0, ...} - 1 {..., ->, -:, -7, 6}

AÇRMAH @MSM^HZ NHATA (A@N)

:¿ Aíth`h?

7¿ Aíth`h?

(@dnhaphsmìîh smauitêedg)

¼@dnhaphebg   ng`g eÿadrh da cgthrds prmahs. ¼^didnmhed   gpdegs hs cgthrds nhaues, nha hs adehrds dxphdetds. ¼H   A@N í h prh`uth `dssds cgthrds sdidnmheg`hs. Dx? A@N (726, :76)? AAN (726, :76) 1 @MSM^ÎH DTNIM@MGEG

ZGNMHEGM^ () Vh`da sdr dsnrmths eg chrag `d uag crgìîh detrd metdmrhs nha `dehameg`hr eîh euih. Dx?

¼r  9 ` ¼Agmhr   rdsth phssávdi? ` - 7

MZZGNMHEG MZZGNM HEGM^ M^ ( ) @ázmags eîh pdrmþ`mngs. Dx? φ, d, 

A@N (726, :76) 1

Pdhrmg Pd hrmg `d nheoueths

:¿ Aíth`h? φ 1

>,7074...

 1 :,, 0, 4} EßADZH @D ^TJNHEOTEPH ^TJNHEOTEPH^? ^?   e ↚ Eÿadrh `d didadeths VZMENÁVMH @G MENIT^ÎH D DRNIT^ÎH

EGPTZGM^ VGZD^ (:e, VGZD^ (:e, e ∂ ) {6, :, 0, 3, 2, ...} EGPTZGM^ ÁAVGZD^ (:e + 7, e ∂ ) {7, >, 4, , 4, , 7, ...} NÇINTIH @H EßADZH @D @MSM^HZD^ @D TA EßADZH EGPTZGI 7. @dnhaphebg h eÿadrh da cgthrds prmahs prmah s (cgthrgr). :. G`mnmhed uag uem`g`d gh dxphdetd `d ng`g cgthr denhetrg`h. >. Auitmpimqud hs rdsuitg`hs gnmag. Dx?

¼H   A@N í `g`h pdih prh`uth `hs tdrahs agrng`hs nha (*). A@N (726, :76) AÁEMAH AßIPMVIH NHATA (AAN) 7¿ Aíth`h?

¼@dnhaphebg   ng`g eÿadrh da cgthrds prmahs. ¼^didnmhed   th`hs hs cgthrds nhaues, nha hs agmhrds dxphdetds. Dx? AAN (726, :76)

HVDZGÌÔD^? Temîh? (G ∯ J)

Metdrsdìîh? (G ∭ J)

@mcdrdeìg? (G - J)

Nhapidadetgr `d G da rdigìîh g J

AAN (726, :76) 1 7

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Cueìîh

WTG@ZH ZD^TAH

@g`hs `hms nheoueths G d J eîh vgzmhs, `mzdahs qud uag rdigìîh y 1 c(x) í uag cueìîh c `d G da J, sd, d shadetd sd, ng`g didadeth x, x ∂  G, nhrrdsphe`dr phr c g ua ÿemnh didadeth y, y ∂ J.

MEDWTGÌÔD^ DRVHEDENMGM^ ¼ ^d g 57? Nhesdrvgahs h smegi `g `dsmlugi`g`d pgrg hs dxphdetds. ¼ ^d 6 9 g 9 7? Mevdrtdahs h smegi `g `dsmlugi`g`d pgrg hs dxphdetds. IHLGZMPAH @demìîh?

Dx? j ↚ Ihlgrmtage`h g ↚ Jgsd x ↚ Sgihr `h ihlgrmtah Nhe`mìôds `d dxmstïenmg @HAÁEMH   @HAÁEMH

@1G

NHEPZG @HAÁEMH  @HAÁEMH 

N@ 1 J

MAGLDA Ma 1 {4, tdahs? ¼ (chl)(x) 1 c(l(x)) 1 :l(x) + 7 1 :(x + >) + 7 1 :x + < ¼ (lhc)(x) 1 l(c(x)) 1 c(x) + > 1 :x + 7 + > 1 :x + 0 ¼^d   g 5 6? Cueìîh nrdsndetd ¼^d   g 9 6? Cueìîh `dnrdsndetd

CTEÌÎH MESDZ^G  MESDZ^G 

CTEÌÎH WTG@ZÇPMNG

LZÇCMNH? VGZÇJHIG ^d g 5 6? Nhengvm`g`d vhitg`g pgrg nmag ^d g 9 6? nhengvm`g`d vhitg`g pgrg jgmxh ZGÁ_D^ (metdrsdìôds ZGÁ_D^  (metdrsdìôds nha h dmxh x)

Cueìîh ihlgrátamng Nçinuih `g Mevdrsg ¼Prhqud   x phr y d y phr x. ¼Mshid   h ehvh y.

CÞZATIG @D JBG^KGZG CTEÌÎH AH@TIGZ ¼Aþ`uih   `d ua eÿadrh rdgi? CTEÌÎH AH@TIGZ JÇ^MNG? ^HAG D VZH@TPH @G^ ZGÁ_D^ x7 d x:

CHZAG CGPHZG@G  G cueìîh qug`rçtmng y 1 gx: + jx + n ph`d sdr dsnrmtg tgajía eg chrag

sde`h x7 d x: gs rgázds SÍZPMND  SÍZPMND 

S 1 (xv, yv)

MEPDZ^DÌÎH NHA H DMRH ]   Í `g`g pdih pheth (6, n) :

Medqugìôds ihlgrátamngs ¼ ^d g 5 7? Nhesdrvgahs h smegi `g `dsmlugi`g`d pgrg hs ihlgrmtage`hs. ¼ ^d 6 9 g 9 7? Mevdrtdahs h smegi `g `dsmlugi`g`d pgrg hs ihlgrmtage`hs.

Agtdaçtmng Nhadrnmgi TEM@G@D^ @D AD@M@G? CTEÌÎH DRVHEDENMGI

Aÿitmpihs

Tem`g`d

Nhaprmadeth

ka

ba

`ga

^updrcánmd

ka

ba

`ga

Shiuad

ka>

ba>

Agssg

kl

Ngpgnm`g`d

kI

:

^ujaÿitmpihs `a

na

aa

a

`a

:

na

aa:

`ga>

a>

`a>

na>

aa>

bl

`gl

l

`l

nl

al

bI

`gI

I

`I

nI

aI

:

:

a :

TEM@G@D^ @D SHITAD 7`a> 1 7 I 7a> 1 7666 I 7 na> 1 7 aI

:

 

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ZG_ÎH (CZGÌÎH) Zgzîh detrd g d j ↚ 

Vrhlrdssîh Grmtaítmng (VG) (VG)

Ldhadtrmg Vigeg

(nha j ≦ 6)

VZHVHZÌÎH Mlugi`g`d `d rgzôds

¼^d   g í `mrdtgadetd prhphrnmhegi g j, tdahs

Ng`g tdrah í hjtm`h pdig shag `h tdrah getdrmhr nha ua vgihr nhestgetd, `dehameg`h rgzîh (r). (g7, g:, g>, ..., ge, ...) Pdahs qud? q ud? g: 1 g7 + r g> 1 g7 + :r , dtn.

PZMÊELTIH

Pdrah Ldrgi (ge) ¼ ^hag `hs êeluihs metdrehs?

¼^d   g í mevdrsgadetd prhphrnmhegi g j, tdahs? ^hag `hs e tdrahs

¼ Êeluih dxtdreh (d) VHZNDEPGLDA (%) Í uag rgzîh dspdnmgi nuoh `dehameg`hr í mlugi g 766. Dx?

N

Pdrah Ldrgi (ge) ^DADIBGEÌG @D PZMÊELTIH^

^hag `hs Pdrahs?

^hag `hs mecmemths tdrahs?

AHEPGEPD (A) OTZH^ NHAVH^PH^

 

LZÇCMNH^

^d

detîh?

Geçimsd Nhajmegtþrmg

Nhaphsths

A

¼ Nhe`mìîh `d dxmstïenmg `d ua trmêeluih

Ng`g tdrah í hjtm`h pdih prh`uth `h tdrah getdrmhr nha ua vgihr nhestgetd, `dehameg`h rgzîh (q). (g7, g:, g>, ..., ge, ...) Pdahs qud? q ud? g: 1 g7 ¼ q g> 1 g7 ¼ q: , dtn.

GTADEPH^ D @D^NHEPH^ Cgthr `d guadeth 1 7 + m Cgthr `d `dsnheth 1 7 „ m m ↚ tgxg (`dnmagi) OTZH^ ^MAVID^ O ↚ Ourhs N ↚ Ngpmtgi memnmgi m ↚ Pgxg `d ourhs (`dnmagi) P ↚ Pdaph

Vrhlrdssîh Ldhaítrmng (VL)

  ^mapids

VZMENÁVMH^ JÇ^MNH^ ^de`h k g rgzîh `d sdadibgeìg tdahs?

¼Vrmenápmh   g`mtmvh? N 7

P

Dstgtástmng

¼Vrmenápmh auitmpimngtmvh hu prmenápmh cue`gadetgi `d nhetglda (V.C.N)? PMVH^ @D GLZTVGADEPH^ ^d g hr`da `hs didadeths í maphrtgetd, tdahs?

PZMÊELTIH ZDPÊELTIH ¼ Zdigìôds aítrmngs

AD@M@G^ @D PDE@ÏENMG NDEPZGI ^dog {x7, x:, x>, ..., xe} ua nheoueth `d `g`hs `demahs? ¼ Aí`mg Grmtaítmng (AG)

Nha Zdpdtmìôds

¼ Aí`mg Ldhaítrmng (AL)

¼ Ad`mgeg (AD) Nhihngahs hs `g`hs da hr`da nrdsndetd. ^d h eÿadrh `d `g`hs í mapgr, g ad`mgeg í h vgihr ndetrgi. ^d h eÿadrh `d `g`hs í pgr, g ad`mgeg í g aí`mg grmtaítmng `hs `hms vgihrds ndetrgms. ¼ Ah`g (Ah) Sgihr agms crdqudetd da ua nheoueth `d `g`hs. AD@M@G^ @D @M^VDZ^ÎH Ad`da g rdluigrm`g`d `h nheoueth `d `g`hs. ¼ Sgrmêenmg (S)

^d g hr`da `hs didadeths eîh í maphrtgetd, tdahs?

¼ Grnhs ehtçvdms (>6¶, 04¿, 36¶)

V(G) ↚ Vrhjgjmim`g`d `d hnhrrdr h dvdeth G e(G) ↚ Eÿadrh `d ngshs cgvhrçvdms (dvdeth) e(D) ↚  Eÿadrh `d ngshs phssávdms (dspgìh gahstrgi)

G@MÌÎH @D VZHJGJMIM@ VZHJGJMIM@G@D^ G@D^ S

04¿

sde

Í g edlgìîh `h dvdeth G ¼ @dsvmh Vg`rîh (ώ)

>6¶

VZHJGJMIM@G@D^

DSDEPH NHAVIDADEPGZ

ώ 1

M) j: 1 g • e MM) n: 1 g • a MMM) b: 1 a • e MS) g • b 1 j • n S) g: 1 j: + n: (Pdhrdag `d Vmtçlhrgs)

nhs tl ZDLZG^ VZÇPMNG^

7

36¶

>

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ZDIGÌÔD^ AÍPZMNG^ ETA PZMÊELTIH WTGIWTDZ ¼ Idm `hs nhssdehs

¼ Idm `hs sdehs

¼ Hutrgs dxprdssôds

ÇZDG^ @D CMLTZG^ VIGEG^ Wug`rg`h

Zdtêeluih

j ⋄b

Vgrgidihlrgah -

NMZNTECDZÏENMG ¼ Êeluihs Prgpízmh

¼ ^dladeth tgeldetd Ihsgelh

VHIÁLHEH^ ¼ ^hag `hs êeluihs metdrehs (^m)

NÁZNTIH PZMÊELTIH^ ¼ Cþrauig jçsmng

¼ ^hag `hs êeluihs dxtdrehs (^d)

¼ Eÿadrh `d `mglhegms

^DPHZ NMZNTIGZ Vhiálheh rdluigr  Vhssum? ¼ Êeluihs   Êeluihs nhelrudetds nhelrudetds detrd sm ¼ Ig`hs nhelrudetds detrd sm Êeluih Metdreh (gm) d êeluih dxtdreh (g d) `d ua phiálheh rdluigr 

¼ Prmêelui Prmêeluih h dqumiçtdrh

0

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^DLADEPH NMZNTIGZ

VMZÊAM@D^

D^CDZG

 GJ

¼ Vmrêam`ds Zdluigrds Dx? Vmrêam`d qug`rgeluigr rdluigr  NHZHG NMZNTIGZ

Ldhadtrmg Gegiátmng VHEPH AÍ@MH @D TA ^DLADEPH

Ldhadtrmg ^þim`g VZM^AG^

¼ Prhenh `d Vmrêam`d @M^PÊENMG DEPZD @HM^ VHEPH^

¼ Vgrgididpápd`h Zdtêeluih

NMIME@ZH

D^PT@H GEGIÁPMNH @G ZDPG ¼ Dqugìîh Zd`uzm`g

Çrdg Phtgi (GP)

Shiuad (S)

@demìîh `d a? Í g tgeldetd `h êeluih chrag`h pdig rdtg d h dmxh x, thag`h eh sdetm`h getm-bhrçrmh.

@mglhegi (@)

NÇINTIH @D a? NHED

NTJH

η

g 

:  

∃y ∃x

4

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DWTGÌÎH CTE@GADEPGI

@M^PÊENMG @D VHEPH G ZDPG

G@MÌÎH @D GZNH^

GZNH @TVIH

Prmlhehadtrmg ZG_ÔD^ PZMLHEHAÍPZMNG^ EH PZMÊELTIH ZDPÊELTIH g j η

n

CTEÌÎH ^DEH DWTGÌÎH LDZGI ZDIGÌÎH CTE@GADEPGI 7

VH^MÌÔD^ ZDIGPMSG^ DEPZD ZDPG^ VGZGIDIG^

NMNIH PZMLHEHAÍPZMNH y

s de de

x

=6 ¿

r 

√7

s 6¿

726¿

nhs

>36¿

x

CTEÌÎH NH^^DEH :