Proof by induction:

Let P(n) be the statement

"any set of n people are the same person".Now, obviously P(1) is true, since in any set of one person, all the members of that set are the same person.

Now, assume that P(n) is true for n = k. Then consider the set of k+1 people. By removing one of these people, we see that the other k people are the same person, by our assumption. Now by placing the removed back in the set and taking another person out, we see that every person in the set is, again, the same person by our assumption. So the collection of k+1 people are all the same person.

So P(1) is true, and P(k)

P(k+1), so any set ofnpeople are, in fact, the same person.

Very funny.

Nice joke. I like things like this.

]]>Let P(n) be the statement *"any set of n people are the same person"*.

Now, obviously P(1) is true, since in any set of one person, all the members of that set are the same person.

Now, assume that P(n) is true for n = k. Then consider the set of k+1 people. By removing one of these people, we see that the other k people are the same person, by our assumption. Now by placing the removed back in the set and taking another person out, we see that every person in the set is, again, the same person by our assumption. So the collection of k+1 people are all the same person.

So P(1) is true, and P(k)

P(k+1), so any set of