Аналитическая геометрия. Шурыгин В.В. - 5 стр.

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x M
x M x ∈ M M 3 x
∅
M
N M
N M ⊂ N N ⊃ M
M N
M = N M = N M ⊂ N
N ⊂ M
M N
M N M N
M ∩ N M N
M ∩N = ∅
M N
M N M N
M ∪N
(x, y) x M
y N
M N M N
M ×N (x, y)
(x, y) 6= (y, x) x 6= y
M N
M ×N = {(x, y) : x ∈ M, y ∈ N}.
   „-8 O618\ )8- x 9b79*8/9) ~7*;*,8-; ;,-|*/8b6 M ‚:-b-398 861|*\ )8-
x .30,6L7*|08 M ƒ -+-[,6 6*8/9 /7*L2J}0; -+36[-;† x ∈ M 070 M 3 x =
   °,-|*/8b-   ,6[b6*8/9 ‰ŠŽ¤‘’\ */70 )0/7- ~7*;*,8-b b ~8-; ;,-|*K
/8b* 1-,*),- = °,-|*/8b- ,6[b6*8/9 ¬Ž‰ŠŽ¤‘’\ */70 )0/7- ~7*;*,8-b
b ~8-; ;,-|*/8b* +*/1-,*),- = ¹-3;67?,- -.3*L*79*8/9 ;,-|*/8b-\ 2 1-K
8-3-:- ,*8 ,0 -L,-:- ~7*;*,86= „61-* ;,-|*/8b- ,6[b6*8/9 ¡œž‘’ ’Šº
»Žž”Š’= ‡79 -+-[,6)*,09 .2/8-:- ;,-|*/8b6 0/.-7?[2*8/9 /0;b-7 ∅ =
   ¼/70 16|LM ~7*;*,8 ;,-|*/8b6 M 9b79*8/9 -L,-b3*;*,,- 0 ~7*;*,K
8-; ;,-|*/8b6 N \ 8- ;,-|*/8b- M ,6[b6*8/9 ¡Šª’Š»Žž”Š’ ;,-|*K
/8b6 N = “8- -+-[,6)6*8/9 /7*L2J}0; -+36[-;† M ⊂ N 070 N ⊃ M = ‡b6
;,-|*/8b6 M 0 N /)086J8/9 -L0,61-b;0 070 /-b.6L6J}0;0\ */70 -,0
/-/8-98 0[ -L,0N 0 8*N |* ~7*;*,8-b= “8- -+-[,6)6*8/9 /7*L2J}0; -+36K
[-;† M = N = ˆ)*b0L,-\ M = N 8-:L6 0 8-7?1- 8-:L6\ 1-:L6 M ⊂ N 0
N ⊂ M=
   —[ 0;*J}0N/9 ;,-|*/8b ;-|,- 1-,/83203-b68? ,-b* ;,-|*/8b6=
   °,-|*/8b-\ /-/8-9}** 0[) b/*N ~7*;*,8-b\ .30,6L7*|6}0N 0 ;,-|*/8b2
M 0 ;,-|*/8b2 N ‚-+}69 6/8? ~80N Lb2N ;,-|*/8bƒ\ ,6[b6*8/9 ¡ŽŽŽº
¤ŽŒŽ’ M 0 N = H*3*/*)*,0* ;,-|*/8b M 0 N -+-[,6)6*8/9 /7*L2J}0;
-+36[-;† M ∩ N = ¼/70 ;,-|*/8b6 M 0 N ,* 0;*J8 -+}0N ~7*;*,8-b\ 0N
.*3*/*)*,0* 9b79*8/9 .2/8; ;,-|*/8b-;† M ∩ N = ∅ =
   °,-|*/8b-\ /-/8-9}** 0[ b/*N ~7*;*,8-b\ .30,6L7*|6}0N 70+- ;,-|*K
/8b2 M 70+- ;,-|*/8b2 N ‚N-89 + -L,-;2 0[ ~80N Lb2N ;,-|*/8bƒ\ ,6[K
b6*8/9 Š¬½ŽªŒŽŒŽ’ M 0 N = ˆ+*L0,*,0* ;,-|*/8b M 0 N -+-[,6)6*8/9
/7*L2J}0; -+36[-;† M ∪ N =
   °,-|*/8b-\ ~7*;*,86;0 1-8-3-:- 9b79J8/9 b/*b-[;-|,* 2.-39L-)*,K
,* .63 (x, y) \ b 1-8-3N .*3bM ~7*;*,8 x .30,6L7*|08 ;,-|*/8b2 M \
6 b8-3-M ~7*;*,8 y .30,6L7*|08 ;,-|*/8b2 N \ ,6[b6*8/9 ¡ŠŒ¢”ŽªŽŒŽ’
         H                                          )
M 0 N = 3-0[b*L*,0* ;,-|*/8b M 0 N -+-[,6 6*8/9 /7*L2J}0; -+36[-;†
         {
M × N = ~8-; -.3*L*7*,00 .63 (x, y) .3*L.-76:6J8/9 2.-39L- *,,;0 =
                                                                     )
“8- -[,6)6*8\ )8- (x, y) 6= (y, x) \ */70 x 6= y = P3681- -.3*L*7*,0* .3-0[b*K
L*,09 ;,-|*/8b M 0 N [6.0/b6*8/9 /7*L2J}0; -+36[-;†
                      M × N = {(x, y) : x ∈ M, y ∈ N }.                    ‚•ƒ
                                      ¾

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