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Mathematics
Set Theory, Logic, Probability, Statistics
Proof of Closed Set by Induction
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[QUOTE="submartingale, post: 3874916, member: 388171"] Hello all, I am trying to prove that a set is closed by induction. Specifically, let me define Let B_t be sets, and A_T:=sum{B_t: t=1, .., T}=Sum{b_t: b_t in B_t, and t=1, ..., T} A property that these sets have is that B_s is a subset of B_t for s<=t. I try to prove A_T is closed by the following argument: 1) First show B_1 is closed. 2) Assume Sum{B_t: t=2, ..., T} is closed. 3) Prove A_T is closed. My question is whether I can assume that Sum{B_t: t=2, ...T} is closed instead of Sum{B_t: t=1, ...T-1} in 2) Thank you in advance [/QUOTE]
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Proof of Closed Set by Induction
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