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ממן12

ממן12 - 12" 1 Y...

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Unformatted text preview: 12 " 1 , Y = {2,3} A - , X = {1,2} A . R = X Y = {(1,2), (1,3), (2,2), ( 2,3)} . K = I A = {(1,1), (2,2), (3,3)} : (1,1) . I A = X Y - A - X , Y . 1 Y 1 X , , X Y - , I A - . (2,2) I A , I A = X Y (2,2) X Y 2 X , 2 Y , . (1,2) I A , (1,2) X Y , , 1 X , 2 Y - X , Y , , I A , . K = X Y - A - .1 .2 2 - n = 0 N , x N - {0} , . x / x = 20 = 1 , 4J 2 , 2,4 N - {0} , : 2J 4 , 4 / 2 = 2 = 21 n = 1 N . , n = -1 , 2 / 4 = 2 -1 = 2 n , 2J 4 , yJx xJy , x, y N - {0} ,- 2 n = 1 / 2 m , y / x = 2 m x / y = 2 n - n, m N n = m = 0 , n, m . n + m = 0 , 2 n +m = 1 = 2 0 . x = y , x / y = 2 0 = 1 , , .1 - n, m N , yJz xJy , ,( ) x / z = 2 n + m , y / z = 2 m x / y = 2 n . xJz , n + m N n, m N . 0 Z ,' , n Z , xKy , x, y N - {0} , - n , n . y / x = 1 / 2 n = 2 - n , . x / y = 2 n - . yKx , 2,4 N - {0} ,- , 1 K - 4 / 2 = 21 4K 2 , -1 Z - 2 / 4 = 2 -1 2K 4 . 2 4 ,' , . n + m Z n, m Z .' , - 4 / 2 = 21 4L 2 , 2,4 N - {0} , : 2L 4 - , 1 N . , n = -1 , 2 / 4 = 2 n = 2 -1 . , 2 / 4 = 1 / 2 = 2 -1 = 3 n . , x / y = 2 n - n N , xLy .- - m N , yLx . x / y = 3 n - n N . y / x = 3 m - n N y / x = 2 m , yLx xLy - , x, y N - {0} : . y / x = 2 m x / y = 2 n , . x = y ,' , 3 n = 1 / 3 m , . y / x = 3 m x / y = 3 n , , . n, m N , n = m = 0 n + m = 0 , 3 n +m = 1 = 30 . x = y , x / y = 3 0 = 1 .3 .2 , 2 n = 1 / 3 m = 3 - m . y / x = 3 m x / y = 2 n , , x / y = 2 0 = 1 , . 2 0 = 1 = 3 0 n = m = 0 . x = y . , 1,2,6 N - {0} , .( 1 N - 2 / 1 = 21 ) 2L1 ,( 1 N - 6 / 2 = 31 ) 6L 2 . 3 n = 6 n , 2 n = 6 n , 6 / 1 = 6 . 6L1 3 : c A , , (a, b) R 2 (1) (a, c) R (2) (c, b) R : d A , (b, a) R 2 - (3) (b, d ) R (4) (d , a) R . , (d , c) R 2 (1)- (4)- , (c, d ) R 2 (3)- (2)- 4 . R = {(1,2), (2,3), (3,1)} : R - R R 2 = {(1,2), (2,3), (3,1)} {(1,3), (2,1), (3,2)} = {(1,2), (1,3), ( 2,1), (2,3), (3,1), (3,2)} (3,1), (1,3) R R 2 , , , . (3,3) R R 2 , , R = {(1,2), (2,3), (3,4), , (n - 3, n - 2), (n - 2, n - 1), (n - 1, n), (n,1)} , nR1 , kRk + 1 k N,1 k n - 1 . R - : , m N,1 < m < n .1 .2 R m = {(1, m + 1), (2, m + 2), , (n - m - 1, n - 1), (n - m, n), , (n - 1, m - 1), (n, m)} : m = k - 1 R k -1 = {(1, k ), ( 2, k + 1), , (n - k - 2, n - 1), (n - k - 1, n), , (n - 1, k - 2), (n, k - 1)} :( ) R R k = {(1, k + 1), (2, k + 2), , (n - k - 1, n - 1), (n - k , n), , (n - 1, k - 1), (n, k )} . ,( 1 ) m A : m = n -1 R n -1 = {(1, n), (2,1), (3,2), , ( n - 1, n - 2), ( n, n - 1)} m , nS1 , , S = R , m =1 n -1 , A n : nSn , 1Sn . n . R = {( x, x + 1) | x N} : R n = {( x, x + n) | x N} . R k = {( x, x + k ) | x N} , k ( x, x + k ) R k , R k +1 = {( x, x + k + 1) | x N} , R - . . ( x + k , x + k + 1) R m ) (0, m), (m, 2m) S . S = R , m =1 n .3 . (0, 2m) S ,( R m - x = 0, x = m 1 k m , (0, 2m) S - : , k, m - , 2m = 0 + k = k , . (0, 2m) R k . m = k = 0 , , m < k : , k . S , (0, 2m) S , 5 , . (b1 , b2 ) E b1 , b2 B , B A / E . B B = B 2 , E B = B B , E B - B - E . E E , A . E B - , E , 2 2 2 . E - 27 . E = 1 + 2 2 + 2 3 = 27 : , ...
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