[Math] Prove or disprove the the floor of xy is equal to the floor of x times the floor of y for all real numbers x and y.

Question

Prove or disprove that $\lfloor$ xy $\rfloor$ = $\lfloor$ x $\rfloor$ $\lfloor$ y $\rfloor$ for all real numbers x and y.

Any advice to get past the mental block I have would be nice. 🙂

Answer 1

I will disprove this claim.

Let x be a real number that equals 1.5.

Let y be a real number that equals 2.

$\lfloor$ (1.5)(2) $\rfloor$ = 3

$\lfloor$ 1.5 $\rfloor$ $\lfloor$ 2 $\rfloor$ = 2

3 does not equal 2, therefore I have found a counterexample.