- #1
alejandro7
- 13
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We define by recursion the set of sets {An:n∈ℕ} this way:
A_0=∅
A_n+1=A_n ∪ {A_n}.
I want to prove by induction that for all n∈ℕ, the set A_n has n elements and that A_n is transitive (i.e. if x∈y∈A_n, then x∈A_n).
My thoughts:
for n=0, A_1 = ∅∪ {∅} = {∅}
then, for n+1: A_n+2 =A_n+1 ∪ {A_n+1}
I'm confused on how to proceed.
A_0=∅
A_n+1=A_n ∪ {A_n}.
I want to prove by induction that for all n∈ℕ, the set A_n has n elements and that A_n is transitive (i.e. if x∈y∈A_n, then x∈A_n).
My thoughts:
for n=0, A_1 = ∅∪ {∅} = {∅}
then, for n+1: A_n+2 =A_n+1 ∪ {A_n+1}
I'm confused on how to proceed.
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