Induction problem: every ball in the collection is white

[JellyFish]

To show: If one ball in a finite collection of balls is white, then every
ball in the collection is white.
Proof: By induction on n, the number of balls in the collection.
Base step: (n = 1) If there is only one ball in a collection of balls
and it happens to be white, then every ball in the collection is white.
Induction hypothesis: If one ball in a collection of n balls is white,
then every ball in the collection is white.
Induction step: Suppose one ball in a given collection of n+1 balls
is white. Form a subcollection of n balls by putting aside one of the
balls not known to be white. This is a collection of n balls, one of
which is white, so by the inductive hypothesis every one of the n balls in
the subcollection is white. Remove one ball from the subcollection and
replace it with the one set aside earlier. This new subcollection is also
collection of n balls, one of which is white, so by the inductive hypothesis
every one of the n balls in the new subcollection is white. Since the two
subcollections between them include every ball in the given collection of
n + 1 balls, every ball in the given collection must be white.
Hence if one ball in a finite collection of balls is white, then every
ball in the collection is white.
Thanks.

 

[stapel]

Review page five of this document. :wink:

 

[galactus]

Pleased do not delete your problem after someone helps solve it. :?: :roll:

It may be of value to someone else later on.