The discussion centers on the mathematical expression for the event that "infinitely many A_i's occur" in a sequence of events {A_1, A_2, ...}. The correct formulation is identified as the intersection of unions, specifically expressed as U(n = 1 to inf, U(m = n to inf, A_m)). A participant argues that the alternative expression U(n = 1 to inf, A_n) is also valid, but this is refuted. The consensus is that the original expression is indeed incorrect, emphasizing the need for precise mathematical notation.
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I believe the original expression, as stated, is incorrect. It should be the intersection of unions, not the union of unions.hholzer said: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?