Boole's Inequality

Hi all,

I was just wondering if anyone knew the proof for boole's inequality

That is P(A1 U A2 U A3 U ... U Ai)<P(A1 + A2 + A3 + .. + Ai)

where u is the union

Thanks

if you mean P(A1 U A2 U...U Ai) <= P(A1) + P(A2) +...+P(Ai)
for n = 2: P(A1 U A2) = P(A1) + P(A2) - P(A ^ B) <= P(A1) + P(A2)
Suppose it holds for n = k. We must proove it for n = k + 1
P(A1 U A2 U...U Ak U Ak+1) = P(UA1..k U Ak+1) <= P(UA1..k) + P(Ak+1) <= P(A1) + P(A2) +...+ P(Ak) + P(Ak+1)

Thanks a lot