# Proofs

• Oct 17th 2008, 01:18 PM
captainjapan
Proofs
Recall that the °oor of a real number x, i.e. [x], is defined to be the largest integer d such that d <= x

Proposition. For any real numbers x and y, [x + y] >= [x] + [y]

(a) Explain briefly why it's not true if you replace >= with =
(b) Prove that this claim is true.
• Oct 17th 2008, 04:39 PM
Plato
a) Suppose that $x=1.9$ and $y=1.8$.