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* .4-5-6 * 2,000 * 12 (2541-2552) * .. .4-5-6
* .4-5-6 * 2,000 * 12 (2541-2552) * .. .4-5-6
Release 2.5 /
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[email protected] http://math.kanuay.com facebook.com/MathEBook
Math E-Book Release 2.5
([email protected]) http://math.kanuay.com thaiware.com Release 1.0 1.8 2547 2548 Release 2.0 2.2.04 2548 2550 Release 2.9 preview 2551 2551 Release 2.5 2554 Release 2.0 Science Center 1 3 2548 2550 O-NET & A-NET 4 2552 O-NET & PAT1 Math E-Book ( ..2537)
. Math E-Book 7 .. Math E-Book
Math E-Book . 738-2-19360-6
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..2551 .4 .6 ()
12 (2541 2552) () (O-NET / PAT1)
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Math E-Book Release 2.5
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. . . () . Science Center
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Thaiware.com, Se-ed.net, f0nt.com ...
[email protected] http://www.facebook.com/MathEBook http://math.kanuay.com :]
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11 . 15 . - 20 . 30 47 . 50 . 55 . 63 . 73 . 81 104 105 . 106 . 113 . 116 . 119 . 125 142 143 . : 144 . : 148 . : 159 . : 161 . : 165 . : 168 . : 171 . 176 197 . 198 . 200
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. 203 . 207 . 212 fog 233 235 . 236 . 238 . 241 . 244 . 246 . 249 . 252 . 253 . 255 273 . 273 . 277 . 279 . 282 () 293 295 . 296 . 300 . 304 . 308 . 310 323 . 324 . 327 . 328 . 330 . 333 . 335 . 338 : 351
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353 . 354 . 357 . 360 . 363 374 375 . 376 . 378 . 380 . 382 395 . 396 . 398 . 401 . 404 . 406 . 410 . 416 . 418 440 441 443 . 443 . 445 . 448 . 451 . 454 . 459 478 479 . 480 . 484 . 497 . 502
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. 508 . 515 535 547 . 547 . 550 . 553
561 1 | 2541 567 2 | 2542 577 3 | 2542 587 4 | 2543 599 5 | 2543 609 6 | 2544 621 7 | 2544 633 8 | 2545 645 9 | 2545 657 0 | 2546 671 ! | 2546 683 @ | 2547 695 # | 2547 709 $ | 2548 721 15 | A-NET 2549 733 16 | A-NET 2550 745 17 | A-NET 2551 757 18 | A-NET 2552 771 25412551 783
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( O-NET)
() ( . .) ( .) ( . .) ( .) ( .) ( . . ) ( . .) ( . . )
(2543-2553)
| 44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Math E-Book Release 2.5
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()
(Set) , 7, 360 , (Element Member)
A, B, C { } (comma) A B 7
A { , , , , , , } B { 2, 1, 0, 1, 2} B {0, 1, 1, 2, 2}
() B
() C {2,5, 2, 3, 3, 2}
C 3 2, 3, 5 C {2, 3,5}
( R2.9pre .4-5-6 )
Math E-Book Release 2.5
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( )
{ 2, 1, 0, 1, 2} {0, 1, 1, 2, 2} C {2, 3,5} D {2,5, 2, 3} C D {a, b, c, d, e} {a, e, i, o, u}
3 ...
E 3 33 E {4,5,6, 7, 8, ..., 32}
E 6 E 29 9, 10, 11, 12, 31
(Finite Set)
X n(X) n(A) 7 , n(B) 5 , n(C) n(D) 3 , n(E) 29
(Null Set Empty Set) { }
n( ) 0
C {2, 3,5} D {2, 3, 7} C D .. C D
S
{ , 0, 1, {2, 3, 4}, {5, {6}},(7,8)} 6 , 0, 1, {2,3,4}, {5,{6}}, (7,8) .. 1 1 1
{(1,2),(2, 1), {1,2}, {2, 1}} 3 (1,2), (2,1), {1,2} .. 1,2 2,1 1,2 2,1
S
{2, 4, ...} 6, 8, 10, 8, 16, 32,
S
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( ) (Infinite Set) F 2, G 0 1
F {1, 0, 1, 2, 3, ...} G
F G
{ | } () ()
G <
Math E-Book Release 2.5
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. B { x x| 7 }
x x 7 B { 2, 1, 0, 1, 2} . 2Z { x | x 4}
2x x 4 x -4, -3, -2, -1, 0, 1, 2, 3, 4 2x Z {0, 1, 4,9, 16}
:
A , 2 B , 3 C , 0.5 G ,
2.5 B , 4 C , 1.5 G 2 B, 3 C, 2.5 B,
() (Relative Universe) U () U U
H { x | x 2 } > { 2, 1, 0, 0.5, 1, 2, 4.5, 7} U H {2, 4.5, 7} U H {2, 3, 4, 5, 6, ...}
( R )
H { x | x 2 } > H { x | x 2 } >R 2 ()
S
()
() , .. ,
15
.
(Subset)
X Y X Y X Y X {1, 2} {0, 1, 2} 1 2 {0, 1, 2}
: () ()
X Y X Y X Y {1, 3} {0, 1, 2} 3 {0, 1, 2} A {m, p, r, w} A
{m} {p} {r} {w} {m, p} {m, r} {m, w} {p, r} {p, w} {r, w} {m, p, r} {m, p, w} {m, r, w} {p, r, w} {m, p, r, w}
A 16 ( ) B B A 16
1. A 2. A A 3. n n2
.. A 16 42 16
A B A B
A B (A B B A)
A A S
S
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( U ) U ( U )
(Proper Subset) n2 1 ( ) A A A A ( < )
(Power Set) A P(A)
A n P(A) n2 A {m, p, r, w} P(A) {m} {p} {r} {w} {m, p} {m, r} ... {m, p, r, w} { , , , , , , , , } 4n(P(A)) 2 16
B A (B A ) B P(A) (B P(A) ) A 16 n(P(A)) 16
1.2
. A {a}
12 2 {a} P(A) { , {a}}
. B {a, b}
22 4 , {a} , {b} {a,b} P(B) { , {a}, {b}, {a, b}}
{a,b, c} A a A b A c A 3 S
{a, b} P(A) {a, b} A .. a A b A 2 S
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. C {2, 3,5}
32 8 , {2} , {3} , {5} , {2, 3} , {2,5} , {3,5} , {2, 3,5} P(C) { , {2}, {3}, {5}, {2, 3}, {2,5}, {3,5}, {2, 3,5}}
. D
02 1 P(D) { }
1.3 E {6, 7} P(E) P(P(E))
P(E) 6 7 {6, 7} { , , , }
P(P(E)) { } {6} {7} {{6, 7}} { ,6} { , 7} { , {6, 7}} {6, 7} {6, {6, 7}} { , , , , , , , , , , {7, {6, 7}} { ,6, 7} { ,6, {6, 7}} { , 7, {6, 7}} {6, 7, {6, 7}} { ,6, 7, {6, 7}} , , , , , }
1.4 F { , 1, {2, 3}}
. 1 F .. 1 F .. ( 1 )
F .. F ..! () { } F .. { } F .. ( F) 2 F .. {2, 3} F .. ( 2 3 F) {2, 3} F .. {{2, 3}} F .. ( {2, 3} F) . 1 P(F) .. (1 P(F) ) {1} P(F) .. {1} F
P(F) .. F { } P(F) .. { } F ( F ) {2, 3} P(F) .. {2, 3} F {{2, 3}} P(F) .. {{2, 3}} F
1.5 A, B A {1, 3,5, 7} B {1,2, 3, 4,5,6, 7}
. X X P(A)
1 X P(A) X A X 42 16
2 4 4 4 4 4 1 4 6 4 10 1 2 3 4
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. X X P(A) n(X) 2<
1 X P(A) X A 16 ( .) n(X) 2< 4 4 4 1 4 60 1 2
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2 X , {1} , {3} , {5} , {7} , {1, 3} , {1,5} , {1, 7} , {3,5} , {3, 7} , {5, 7} 11
. Y A Y Y B
A Y 1, 3, 5, 7 Y () Y B 2, 4, 6 Y ( 1, 3, 5, 7 Y B )
2, 4, 6 Y {2, 4,6}
32 8
8 Y {1, 3,5, 7} , {1, 3,5, 7,2} , {1, 3,5, 7, 4} , {1, 3,5, 7,6} , {1, 3,5, 7,2, 4} , {1, 3,5, 7,2,6} , {1, 3,5, 7, 4,6} , {1, 3,5, 7,2, 4,6}
. (1) (1.1) {a, {b, c}} (1.9) {a, {b, c}} (1.2) a {a, {b, c}} (1.10) a {a, {b, c}} (1.3) b {a, {b, c}} (1.11) b {a, {b, c}} (1.4) {a} {a, {b, c}} (1.12) {a} {a, {b, c}} (1.5) {b} {a, {b, c}} (1.13) {b} {a, {b, c}} (1.6) {b, c} {a, {b, c}} (1.14) {b, c} {a, {b, c}} (1.7) {{b, c}} {a, {b, c}} (1.15) {{b, c}} {a, {b, c}} (1.8) {a, {b, c}} {a, {b, c}} (1.16) {a, {b, c}} {a, {b, c}} (2) (2.1) { , 0, 1, {1}, {0, 1}} (2.7) { , 0, 1, {1}, {0, 1}} (2.2) {0} { , 0, 1, {1}, {0, 1}} (2.8) {0} { , 0, 1, {1}, {0, 1}} (2.3) {1} { , 0, 1, {1}, {0, 1}} (2.9) {1} { , 0, 1, {1}, {0, 1}} (2.4) {0, 1} { , 0, 1, {1}, {0, 1}} (2.10) {0, 1} { , 0, 1, {1}, {0, 1}} (2.5) {0, {1}} { , 0, 1, {1}, {0, 1}} (2.11) {0, {1}} { , 0, 1, {1}, {0, 1}} (2.6) {{0, 1}} { , 0, 1, {1}, {0, 1}} (2.12) {{0, 1}} { , 0, 1, {1}, {0, 1}}
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(3) A {{ }, a, b, {a}, {a, b}} (3.1) { } A (3.3) {{a}, b} A (3.2) { } A (3.4) {a, b} A {a, b} A (4) A { , a, {b}, {a, b}} (4.1) P(A) (4.6) a P(A) (4.2) { } P