An expression for a sequence of events

[hholzer]

if you have a sequence of events {A_1, A_2, ...} then an expression
for the event that "infinitely many A_i's occur" is:

U(n = 1 to inf, U(m = n to inf, A_m) )

but wouldn't

U(n = 1 to inf, A_n)

also satisfy this?

 

[mathman]

if you have a sequence of events {A_1, A_2, ...} then an expression
for the event that "infinitely many A_i's occur" is:

U(n = 1 to inf, U(m = n to inf, A_m) )

but wouldn't

U(n = 1 to inf, A_n)

also satisfy this?

I believe the original expression, as stated, is incorrect. It should be the intersection of unions, not the union of unions.