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From: agapito6314 on 26 Jul 2010 13:37
Let {A_k} be a sequence of sets. Let E_n = UNION A_k, k in [1,n],
and E_0 = emptyset

Let F_n = A_n \ E_(n-1) for all n.

If x is in A_k for some k in [1,n], how can one show there exits a
j in [1,n] such that x is in F_j? Can it be done without using
induction? Many thanks in advance.

From: FredJeffries on 26 Jul 2010 15:07
On Jul 26, 10:37 am, agapito6...(a)aol.com wrote:
> Let {A_k} be a sequence of sets.  Let  E_n = UNION A_k,  k in [1,n],
> and E_0 = emptyset
>
> Let  F_n =  A_n \ E_(n-1) for all n.
>
> If x is in A_k  for some k in [1,n],  how can one show there exits a
> j  in [1,n] such that x  is in F_j?  Can it be done without using
> induction?  Many thanks in advance.

Hint: Let j be the first index number in [1,n] such that A_j contains
x.
From: agapito6314 on 26 Jul 2010 15:37
On Jul 26, 2:07 pm, FredJeffries <fredjeffr...(a)gmail.com> wrote:
> On Jul 26, 10:37 am, agapito6...(a)aol.com wrote:
>
> > Let {A_k} be a sequence of sets.  Let  E_n = UNION A_k,  k in [1,n],
> > and E_0 = emptyset
>
> > Let  F_n =  A_n \ E_(n-1) for all n.
>
> > If x is in A_k  for some k in [1,n],  how can one show there exits a
> > j  in [1,n] such that x  is in F_j?  Can it be done without using
> > induction?  Many thanks in advance.
>
> Hint: Let j be the first index number in [1,n] such that A_j contains
> x.

Of course, many thanks for your help!
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