An expression for a sequence of events

  • Thread starter hholzer
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  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
mathman
Science Advisor
7,801
431
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.
 

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