probabilitats

P[ 0 [< y+(-x) [< nx ] = (1/(n+1)) [< 1

x [< y [< (n+1)·x

P[ 0 [< y+(-1) [< f(x) ] = ( 1/(f(x)+1) ) [< 1

1 [< y [< f(x)+1

0 [< f(x)

P[ 0 [< y+(-x) [< f(x) & 0 [< x ] = ( x/(f(x)+x) ) [< 1

x [< y [< f(x)+x

0 [< f(x)

P[ 0 [< y+(-1)·x^{n} [< f(x) & 0 [< x^{n} ] = ( x^{n}/(f(x)+x^{n}) ) [< 1

x^{n} [< y [< f(x)+x^{n}

0 [< f(x)

P[ (-x)+c = x+(-a) & (-y)+c = y & 0 [< a ] = ( c/(c+a) ) [< 1

(-x)+c = x+(-a) <==> x = ( (c+a)/2 )

(-y)+c = y <==> y = ( c/2 )

P[ (-x)+c = x+(-a) & (-y)+c = y+(-b) & 0 [< b [< a ] = ( (c+b)/(c+a) ) [< 1

(-x)+c = x+(-a) <==> x = ( (c+a)/2 )

(-y)+c = y+(-b) <==> y = ( (c+b)/2 )

P[ x^{n+1} = ax^{n} & y^{n+1} = by^{n} & 0 [< b [< a  ] = (b/a) [< 1

x = a & y = b

P[ x^{(-n)+(-1)} = ax^{(-n)} & y^{(-n)+(-1)} = by^{(-n)} & 0 [< (1/b) [< (1/a) ] = (a/b) [< 1

x = (1/a) & y = (1/b)

P[ 1 < x ] = ( (x+(-1))/(x+1) ) [< 1

(x+(-1)) [< x [< (x+1)

0 [< (x+(-1))·(x+1) [< x·(x+1) [< (x+1)^{2}

P[ (-1) > x ] = ( (x+1)/(x+(-1)) ) [< 1

(x+(-1)) [< x [< (x+1)

(x+(-1))^{2} >] x·(x+(-1)) >] (x+1)·(x+(-1)) >] 0