1
픡숡
1.1
줡픢
줡픢: 씡딡 젡갡씢 육픡씣 괡 댡쀡윢 봡먡휡 젢픢 숡 윣윢 딢 괡 댡쀡됡육 먢윤
(1) N : 윥씤숡 젣찡육 줡픣
(2) Z : 젢숡 젣찡육 줡픣
(3) Q : 윦뤡숡 젣찡육 줡픣
(4) R : 숢숡 젣찡육 줡픣
(5) R+ : 씥육 숢숡 젣찡육 줡픣 (0 →
/ R+ )
(6) C : 밡섡숡 젣찡육 줡픣
젡육. 됢 줡픣 X옡 Y 씢 댡픡씣
X ↑ Y = {(x, y) | x → X, y → Y }
옡젢.
1.2
픡숡육 젡육
픡숡: 갡줡픡육 씡눡 됡 줡픡 X, Y 씢 댡픢씣 픣숡 f : X → Y 눢 X윢 갢 옡섡 x ↑ X씢 Y
윢 옡섡 f (x) ↑ Y 뤡 옢줢 픢뀡씤 댡윣숢퀡눢 갣
옡젢.
픡숡육 괡뜡픢(graph)
{(x, f (x)) | x ↑ X} ↓ X ↔ Y
옡젡.
픡숡 f : X → Y 갡 육윢딡,
• f 윣 측씡(range, image) = 픡숡갢됡 젡찡윣 줡픢 = {f (x) | x ↑ X}
• f 갡 젡쀡(surjective)픡숡윤눡 = 갣씡갤 측씡윤 갥윢 딡
• f 갡 육댡육픡숡(눢쀡, injective)
1.3
픡숡육 묡봡밡
젡육. 픡숡 y = f (x)육 x = a씡섡육 묡봡갡숡눡
f (a + h) → f (a)
f (x) → f (a)
= lim
x↑a
h↑0
h
x→a
f → (a) = lim
윢눢.
젡뤡. 픡숡 y = f (x)갡 x = a씡섡 묡봡갡눡픢먡 f 눢 x = a씡섡 씢섢육눣.
묡봡갡눣픢 픡숡 f (x)육 댡픡숡
d
f (x + h) → f (x)
f (x) = f → (x) = lim
h↑0
dx
h
갡육 묡봡밡 (됡 픡숡 f (x)옡 g(x)갡 묡봡갡눣픣 딡)
됡 픡숡육 갢 y = f (x)g(x)육 댡픡숡
먡육 묡봡밡 (됡 픡숡 f (x)옡 g(x)갡 묡봡갡눣픤갣 g(x) ↑= 0윣 딡)
1
픡숡 y = g(x)
육 댡픡숡
(x)
픡숡 y = fg(x)
육 댡픡숡
픡섡픢숡육 묡봡밡 (됡 픡숡 f (x)옡 g(x)갡 묡봡갡눡픢 딡)
픣섡픡숡 y = f (g(x))육 댡픡숡
0