This week's giveaway is in the EJB and other Java EE Technologies forum.
We're giving away four copies of EJB 3 in Action and have Debu Panda, Reza Rahman, Ryan Cuprak, and Michael Remijan on-line!
See this thread for details.
The moose likes Programming Diversions and the fly likes Whats wrong with this proof? Big Moose Saloon
  Search | Java FAQ | Recent Topics | Flagged Topics | Hot Topics | Zero Replies
Register / Login


Win a copy of EJB 3 in Action this week in the EJB and other Java EE Technologies forum!
JavaRanch » Java Forums » Other » Programming Diversions
Bookmark "Whats wrong with this proof?" Watch "Whats wrong with this proof?" New topic
Author

Whats wrong with this proof?

Arjun Shastry
Ranch Hand

Joined: Mar 13, 2003
Posts: 1871
Theorem: All horses are of the same colour.
Proof: We prove this by induction on the number of horses in a group.
For n = 1, there is only one horse and hence nothing to prove.
Assume that given any group of n horses, all are of the same colour.
To prove the above statement for n + 1, consider a group of n + 1 horses.
Remove one horse from the group. Then, by assumption, remaining n horses
are of the same colour. Replace the horse and remove another one from the
group. Now the remaining n are of the same colour. Hence all the n + 1 horses are of the same colour.
[ October 15, 2003: Message edited by: Capablanca Kepler ]

MH
fred rosenberger
lowercase baba
Bartender

Joined: Oct 02, 2003
Posts: 10911
    
  12

This is easy. It fails when we have two horses.
remove 1 horse. we have one left, and it must be the same color as itself.
replace that one, and remove the other. it must be the same color as itself.
BUT, there is nothing connecting the two sets togther. you have not proved that there is a RELATIONSHIP between the two groups.
in other words, the color of one horse has no bearing on the color of another.
[ October 16, 2003: Message edited by: fred rosenberger ]

There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Arjun Shastry
Ranch Hand

Joined: Mar 13, 2003
Posts: 1871
 
I agree. Here's the link: http://aspose.com/file-tools
 
subject: Whats wrong with this proof?
 
Similar Threads
over loaded methods??
25 horses to win, place, show
Another horse race
Descending order and associating Array Elements in sort method to another's elements
Different Colour for different group of overlapping circles.