desigualtats

Si 0 < a < b < 1 ==> 0 < a^{2} < ab < b^{2} < 1


0 < a < b < 1
0 < a^{2} < ab < a < 1
0 < ab < b^{2} < b < 1


Si 0 < a < b < 1 ==> 0 < 2a < a+b < 2b < 2


0 < a < b < 1
a+0 < a+a < a+b < a+1
b+0 < a+b < b+b < b+1 < 1+1 = 2


Si 0 < a < b < 1 ==> 0 < (n+1)a < na+b < a+nb < (n+1)b < (n+1)


0 < a < b < 1
(n+(-1))·0 < (n+(-1))a < (n+(-1))b < (n+(-1))
na+0 < na+a < na+b < na+1
nb+0 < a+nb < nb+b < nb+1 < n+1