Re: Question about induction argument

From: Agapito Martinez (agapito6314_at_aol.com)
Date: 10/07/04 

Date: 6 Oct 2004 19:01:11 -0700

"Stephen J. Herschkorn" <herschko@rutcor.rutgers.edu> wrote in message news:<4164325F.1080108@rutcor.rutgers.edu>...
> Agapito Martinez wrote:
>
> >Consider interval [a_0, b_0]. There is a collection {(a_j, b_j):
> >1<=j<=n} of (open) intervals such that
> >
> >Union (j=1 -> n) (a_j, b_j) contains [a_0, b_0].
> >
> >It is intuitively clear that there exists a subset of {(a_j, b_j)},
> >{(a_k, b_k): 1<= k <= m <= n} such that :
> >
> >a_1 < a_0 < b_1, a_m < b_0 < b_m and
> >
> >for m>1, a_(k+1) < b_k < b_(k+1), 1 <= k <= m-1
> >
> >How does one construct a formal induction argument to prove this?
> >
> >
>
> Huh? No induction needed. {(a0-1, b0+1)} does the trick.

Many thanks Dr. H. but I'm afraid I don't understand. Can you please
elaborate a little. Again, many thanks am