0.4 + 0.2 == 0.6

False

a = 0.4
b = 0.2
print(1/(a+b-0.6))

9007199254740992.0

2/3 == 1- 1/3

False

0.1+0.2

0.30000000000000004

Exemple proposé par M. Colonna, de l'Ecole Polytechnique (source : mooc Fun "Polytechnique #Genius : promenades mathématiques")

$B = 4095.1$

$A = B+1$

$X_0 = 1$

$X_1 = A\times X_0 - B$

$X_2 = A\times X_1 - B$

$X_3 = A\times X_2 - B$

...

B = 4095.1
A = B+1
X = 1
for i in range(7):
    X = A*X-B
    print('X', i+1 , ' = ', X)

X 1  =  1.0000000000004547
X 2  =  1.0000000018631
X 3  =  1.0000076314440776
X 4  =  1.0312591580864137
X 5  =  129.04063743775941
X 6  =  524468.2550088064
X 7  =  2148270324.241572