MeLhem-abrcqL Indr;ct^ron
cryr be used lro
ts bh"V asserb bhab
n) rs Lrug
Prhqstr- -d--nl4heLuale caL tnducbfo n
-_6;:v"" 'rrrr-
Easis sLep g Pca) is brue-
,b sk,o z Vn e 7/.'
( Pch> -> Fr,htr > )
Pcrl nVn Rnr
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Mathematical Induction, Lecture notes of Discrete Structures and Graph Theory
Lecture note from my discrete structure class in Chulalongkorn University
Typology: Lecture notes
2019/2020
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MeLhem-abrcqL Indr;ct^ron cryr (^) be used lro
ts bh"V asserb^ bhab
n) rs Lrug
Prhqstr-
-d--nl4heLuale caL tnducbfo n -_6;:v"" 'rrrr- Easis sLep g^ Pca)^ is^ brue- ,b (^) sk,o z Vn e (^) 7/.'
( Pch>
->
Fr,htr > )
Pcrl (^) nVn Rnr
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Ver ln ar
t .cor, t^ arn+t-^ a)^ /cr-r>
v{nore
Vn, lt 2 ^ ZL+nu.^ zh
= en*1^ r =Q ot 2 -t zL Assume Pcn>. : =Pcn) P (^) l-h C?L
2l=
2o* (^) 24* ^ 2' n (^) 2^"
n*l
-t +
ntt
?- 2ntz
E (^) Z(n+r)+ I n+l
Yr> t^ Ln-si]) ,. "Pc"rn
h: Pc r
Stnce +22L Nehzitu (^) Vo VF>n (,^ Pch) -? Fclor, (^) ) A ssurn^ e, Pc h> Crrnsider a
S ho':r l2c^ lztr^ I^
h+L e o htt herr hre^ \ovo P^ C}l+r-) t< (^) 2}.
Lt"al: Ir 7t i.+tn
77 4_ t t/l
Basfs 6Ie ; Cn?o ) show^7 4.+
H (^) o: H !1^ t+o =, lto sume. [t h.>ro 1{r :^ {.tL+ L t-.-" ^l- ")
Amsider +^ t +..- +^ t
zr<-+1 z^ "ht t .:: (^) t+t+...t 1- .t 'l (^). +.-.t 4
2V*t ,E,r
1+ E {^ r ..-f^4 w
2n (^) + 7 t^ rB^ + 2h q^ t + (h+1^ I
10 Ilnn_Lorybey (^) srbsehs n): v (^) rl l- r14l l'€-^ SeuL -" -B-e-rrs oleg (^) e shoLPc-E) , H?o
gh oh ererrrl ;ubse[s
,
-A
]2s-a eLLuJh IvU l'{-t L (^) ul"^"r l-, (^). -'rhla,n -3" = s'-q-[eJ^ u0le.rre a^ e^ I ' o st^ has^ h^ eleunen*s. t__
- _---_Iunsrc)r:r-T u Arb qk1 (^) ru Surs---L4-s!--a-u--eaag]rbs r4s^4 S'.- l^L r r-^ t- l'-0 at O 4 a-,,ui"Tula-@ o &_r lq, "t tlL (^) .h;. ,rbb, wrg a (^) s.rb s ---u---O "l S /- , A^ b
11
TNDUCTTaN
lbe.h--&ru-+b-nud (^) _ o. (^) ( (^) Pc ):eUre -*q-_ELI-_e_e
LE- (^) L ALn 1"€rr_se!0$e__rrJ}rl_ __ (^) __ _- as (^) & (^) _pcaeLec.t ---i *sen-Lrylthnes
,.,fl*--ee -pced,rvt
d grrircs_*_
DletL -Ls -cr/{}
Fo itln ,^ _^ _. (^3) orb (^) e'Z' (^) ?-= .l__arb^ , 4 qv_g,h l&eiL h:tr =-Br b En{!l (^) }he