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Proof By Induction

  1. Apr 20, 2012 #1
    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
  2. jcsd
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