ѧŤʤѺ

Եʵ ѧѹ ѹ ҡ ˹ () ѧա૵˹ ( ù) ·Ҫԡ˹ӡѹ ԴǺʹͧѧѹ繾鹰ҹͧءҢҢͧԵʵԷʵԧҳ

ǤԴӤѭش ѧѹ '' ˹ Ѿ¢鹡Ѻ觷 仹繵ҧ

  • Фշ赹ͺ (ᴧ, , ͧ, , , Թ, ǧ) շͺ繿ѧѹͧФ 칪ͺᴧ ͺǧ 㹷觷Ҥͤ мѾ 1 8 մѧ
  • 硺ҧ¹й㹪ǧĴ͹ ӹǹйǷ繿ѧѹͧس¹͡ ҧ ¹͡س 85 ͧ Т 10 س 95 ͧ Т 25 㹷 觷Ҥس мѾͨӹǹйǷ
  • ͹Թ͹˹觻ŧҨҡ鹵ҧͧ֡٧ һ¨ҡ鹷ͧ 2 Թҷ жһ¨ҡ鹷Ỵ (§) 4 Թҷ 㹷 觹Ҥͪ мѾԹҷ ѧѹ͸Ժ¤ѹҧ ҷ͹Թ鵡֧鹡Ѻ鹷ѹ١ŧ ( )

'' ѧѹҨ ٵ, ѹ (Եʵ) ҧӴѺѾѺ觷 ѡɳ੾зӤѭͧѧѹѹռѾ͹ʹ觹͹ ѡɳйººѧѹѺ 'ͧ' 'ͧ' ¹觹繼Ѿµ ѡ¡觹 (argument) ¡Ѿ (value) ͧѧѹ

ԴͧѧѹԴҡФҢͧѧѹ繵Ţ駤 ѹͧѧѹѡ¹ٻٵ ШҢͧѧѹҷѹ§᷹ŧٵ

f(x) = x2

觨ҡѧͧͧ x

¹· ѧѹöҡ˹

g(x,y) = xy

繿ѧѹӵŢ x y ҼŤٳ ͹ҹѧѹԧѧ͸Ժ¢ҧ '' Ѻ觹 2 ҧá ҤԴ觹 2 觹 ѹѺ (x,y) 1 ҡö g 繿ѧѹ ·ͤѹѺ (x,y) ФҢͧѧѹ xy

Էʵ ѡеͧ༪ԭ˹ҡѺѧѹ˹鹨ҡٵ سԺ鹼š˹ 繿ѧѹʶҹ ѾسԢͧʶҹҹ

ǤԴͧѧѹӡѴäӹdzµŢҹ ӡѴäӹdz ǤԴͧԵʵǡѺѧѹ ǤԴ·ӡѴʶҹóǢͧѺŢҹ ͹ҿѧѹ§ '' (૵ͧ觹) ҡѺ '' (૵ͧѾ) ѧҪԡеǢͧШѺѺҪԡ㴵˹觢ͧҹ ѧѹ鹹繤ѹ͹ ѧСǵ ˵بҡѡɳз仹 ǤԴǺʹͧѧѹ֧繾鹰ҹͧءҢ㹤Եʵ

ѵ

㹷ҧԵʵ 'ѧѹ' ѭѵԢ źԫ .. 2237 ͸Ժ»ҳǢͧѺ ѹͧ ش ѧѹźԫԨóҹ㹻Ѩغѹ¡ ѧѹ͹ؾѹ 繪Դͧѧѹѡ¼ѡԵʵ ѺѧѹԴ öٴ֧Ե͹ؾѹɮ૵ ǡѵطҧԵʵ Ԥŷ źિʡ ͧѧѹ͡ͺѹ

㹤ӹ ѧѹ§óվɢͧѹ ҧá 繡óշդʹ繾 ᵡҧҧӹѺӹͧ硹ҡ

ǤԴͧ ѧѹ 繡㹡äӹdz ᷹繤ѹ쪹Դɹ Եáʵ Էҡäԧɮ к 件֧ Ť ɮѧѹ¹Դ ͧѡ÷ԧ

ҧ繷ҧ

ѧѹ f ҡŹ૵ X ѧŷ૵ Y) ѹ ҧ X Ѻ Y

  1. Ѻء x X y Y x f y (x դѹ f Ѻ y) 蹤 ѺҹФ ռѾ Y ҧ 1 Ѿ
  2. x f y x f z y = z 蹤 ҹ¤öռѾ ҹҤöռѾ¼Ѿ

ҹ x Ф ҡ ռѾ y ҡ§ ᷹ f (x)

ҡҧ ö¹ҧ ѧѹҡ X ѧ Y f ͧŤٳ¹ ·ФҢͧ x X y Y ᵡҧѹ ·ѹѺ (x, y) f

૵ͧѧѹ ءѧѹ᷹ YX ѧࡵ |YX|=|Y||X| (ҧ֧ ӹǹԧùѺ)

ѹҧ X Ѻ Y 仵͹ (1) 蹤ѧѹ¤ ѧѹءѧѹ繿ѧѹ¤ ѧѹ¤ءѧѹ繿ѧѹ ѹҧ X Ѻ Y 仵͹ (2) 蹤ѧѹҧǹ ѧѹءѧѹ繿ѧѹҧǹ ѧѹҧǹءѧѹ繿ѧѹ 'ѧѹ' ͤѹ仵͹䢷ͧ͹

ٵҧ仹

Ҫԡ 3 X ѹѺ b c Y ѹ繿ѧѹ¤ 繿ѧѹ

Ҫԡ 1 X ѹѺҪԡ Y ѹ繿ѧѹҧǹ 繿ѧѹ

ѹ繿ѧѹҡ X ѧ Y öҹѧѹҧѴ f={ (1,d) , (2,d) , (3,c) }

, ù

X 觤૵Ź¡ ͧ f Y 觤૵ͧѾ ¡ ùͧ f ૵ͧѾԧ {f (x): x } ѧҺҧж١¡ù ͧҡԴҴҡèṡҧŷѺŨԧ

ѧѹ¡͵ùͧѹ ѧѹӹǹԧ ѧѹӹǹԧ͹

͹ⴿѧѹ Ϳѧѹù૵ǡѹ

ҢԷҡä ẺԴͧФҷ׹Ѻк (ӴѺ) ͧ ѧж١˹пѧѹ ùǡѺҤҷ׹ѺҨҧ

ѧѹ˹觵˹ ѧѹǶ֧ пѧѹ˹觵˹觷Ƕ֧

ö觿ѧѹѡɳФѹѧ

  • ѧѹ˹觵˹ (1-1) ѧѹФ׹ҷ͹ѹҡҤҤФҡѹ Ǥ x1 x2 Ҫԡͧͧ f f (x1) = f (x2) x1 = x2
  • ѧѹǶ֧ (Ẻ onto) ѧѹùҡѺ Ǥ y Ҫԡͧͧ f Ǩ x ҧ 1 f (x) = y

Ҿ кؾҾ

Ҿ (image) ͧҪԡ xX f ͼѾ f (x)

Ҿͧ૵ AX fY չѧ

f[A]={f (x) |xA}

ҧ Ҩ f (A) ᷹ f[A]

ѧࡵùͧ f Ҿ f (X) ͧͧѹ. 㹿ѧѹҧ Ҿͧ {2, 3} f f ({2, 3}) = {c, d} ùͧ f {c, d}

ؾҾ (preimage) ( Ҿѹ) ͧ૵ BY f ૵¢ͧ X չ

f−1 (B) = {x X | f (x) ∈B}

Ѻѧѹҧ ؾҾͧ {a, b} f−1 ({a, b}) = {1}

ҿͧѧѹ

ҿͧѧѹ f ૵ͧѹѺ (x, f (x)) Ѻ x X շɮպʴ;٨ҡҿ ɮպҿԴ X Y 鹨ӹǹԧ ǹʹͧѺǤԴͧҿ

ҿͧѧѹѧ ҿ繿ѧѹǶ֧繿ѧѹ˹觵˹

ѧࡵͤѹҧͧ૵ X Y ѡʴ૵¢ͧ X×Y ҧ繷ҧâͧѧѹкؿѧѹ f ¡ҿͧѹ

ҧѧѹ

  • ѹ wght ҧؤšѺ˹ѡ˹
  • ѹ cap ҧȡѺͧǧͧȹ
  • ѹ sqr ҧӹǹҵ n Ѻѧͧ n2
  • ѹ ln ҧӹǹԧǡ x Ѻ͡Էҹҵ ln (x) ѹҧӹǹԧѺ͡ԷҹҵԹ繿ѧѹ Ҩӹǹԧءӹǹ͡Էҹҵ 蹤繤ѹ
  • ѹ dist ҧشйҺ R2 ѺзҧҡشԴ (0,0)

ԴͧѧѹҧԵʵѡѹ úǡ ź äٳ ع Ţ¡ѧ ͡Է ҡ ѵǹ ⡳Ե ѧѹҹѡ¡ ѧѹ鹰ҹ ӹդµҧ͡仵ҢҢͧԵʵ ҧͧѧѹ繾鹰ҹ (ѧѹ) ѧѹ ѧѹ



سѵԢͧѧѹ

ѧѹҨ

ѧѹẺ n-ary: ѧѹµ

ѧѹǹѡ ѧѹµ ҷТѺѨµҧѹ ҡͧͧԵʵ ÷ͧʴҧѴͷԴѹẺѧѹ - ջѨ '͹' 蹡ѹ ҡͧͧԵʵ դᵡҧԧسҾҧѧѹǡѺѧѹµ ѧѹèӹǹԧ鹡Ϳѧѹͧ triple ((x,y,z)) ͧӹǹԧ

ͧѧѹ˹૵¢ͧ Ťٳ¹ ͧ n ૵ ¡ѧѹ ѧѹ n-ary ҧ蹿ѧѹ dist ֧ѧѹҤ 㹡óչ dist ((x,y)) ¹ҧ dist (x,y)

ôԹ 繿ѧѹµêԴ˹ ժԵ ǴԹ '*' 鹹ҡѧѹҤ ¹ٵ x*y Ңҹ ͹Ѻ¡ѧѹ * (x,y) » §¹ٻѭóҧ (infix notation) дǡ

ҧӤѭҧɮյҧ˹觤 ˹ԧѧѹ ǤԴͧѧѹٹҧ Ըչ èѴѧѹµ͹繡ôԹ Ť ҡѹ (syntax)

ûСͺѧѹ

ѧѹ f: Xye → Y g:YZ öСͺѹ 觨ѧѹСͺ g o f: XZ չ (g o f) (x) = g (f (x)) ѺءҢͧ x X ҧ Ҥ٧ͧͧԹ t 仵ѧѹ h (t) Ф鹢ͧ͡ਹҡȷ٧ x 仵ѧѹ c (x) ѧ (c o h) (t) к͡鹢ͧ͡ਹҡͺͧԹ t

ѧѹѹ

ҿѧѹ f: XY ѧѹ˹觵˹觵ͧ ͧҪԡ y Y ૵ⷹ ѧѹҡ yY ѧ f −1 (y) ͧѹ Ϳѧѹ¡ ѧѹѹ ͧ f ¹᷹ f −1

ҧ˹觢ͧѧѹѹѺ f (x) = 2x f −1 (x) = x/2 ѧѹѹͿѧѹ͹áзӢͧѧѹẺͧѹ ѹ

ҧ駿ѧѹѹҡ Ԩó f(x) = x2 ѧѹ ѧѹѹͧ f

ٻҾǢͧ

Ԫ


ͧṹ ?

ҧ :


Boom-Elec

ʶҹ :
硷͹ԡ