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., ., ., " "(2000)

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3 + 6 = 9, .

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x + 9 = 0, x = 9 . ( p)

p(x)- .

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- , , x : p(x) -x- . - x : p(x) -p(x) x .

x : x + 9 = 0 - x : x + 9 = 0 - .

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p,q .

p ,

p- p .

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p p

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p,q

, p q (p q) . , p q (p q).

p q , p q (p-q , p q ) .

p q ( )

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p q p q p q p q

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p,q r .

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:p p :p q q p, p q q p :p (q r) (p q) r , p (q r) (p q) r :p (q r) (pq) (p r), p (q r) (pq) (p r) :p q p q, p q p q. 1

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N = {1, 2, 3, ...} ,Z = {...,3,2,1, 0, 1, 2, 3, ...} , [a, b]

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(1) : M = {a, b, c , ...}(2)

: M = {x |A(x) is true}. 1

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a A a A, a / A.A = {a1, a2, ..., an} a1, a2, ..., an A .

. . . 6= {0} .

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A = {x R|x2 + 1 = 0} = - N0 = {0, 1, 2, . . .} - M = {1, 12 , 13 , . . .} - B = {x R|0 x 1} -

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M N (x M x N) M N - .

M N M N- .M N (M N) (x N; x / M) - .

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(i) M M (ii) (M N) (N P) M P (iii) (M N) (N M) M = N

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M,N .

M N M N .

M N := {x |(x M) (x N)} M N M N .

M N := {x |(x M) (x N)} M- N N M .

M \ N = {x |x M x / N} M- (M )M = \M. 1

A,B,C X . X \ (X \ A) = A A B = B A, A B = B A A (B C ) = (A B) C , A (B C ) = (A B) C

A(BC ) = (AB)(AC ), A(BC ) = (AB)(AC )

A = A, A = X \(AB) = A B = AB, X \(AB) = (X \A)(X \B) Aj j J ( ) :jJAj := {x |j J; x Aj}; jJAj := {x |j J; x Aj}. 1

M

P(M) := {A | A M}

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X, Y .

x X , y Y x , y (x , y) - . (x , y), (z ,w)

x = z y = w .X, Y

X Y - .X Y := {(x , y) | x X y Y } n . Xi (i = 1, n) :

ni=1

Xi = X1 X2 . . .Xn := {(x1, x2, . . . xn) | xi Xi ; i = 1, n}

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N = {1, 2, 3, . . .} N0 = {0, 1, 2, 3, . . .}a, b N a + b N, a b N Z = {. . . 3,2,1} Na, b Z a + b Z , a b Z , a b Z Q = { ab | a Z b N}a, b Q a b Q, a b Q, ab Q, b 6= 0 R = Q I (I )

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, .

. a, b, c R : a + b = b + a a + (b + c) = (a + b) + c 0 + a = a + 0 = a a + x = 0 a - x . ab = ba a(bc) = (ab)c (a + b)c = ac + bc 1 a = a 1 = a a R \ {0} a x = 1 x .

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a < b, a + c < b + c c R a < b, ac < bc c > 0 (a < b) (b < c) a < c :

a, b R : a < b c R a < c < b :

x , y > 0 n N : nx > y

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