Math Is Fun Forum

Dross

Member

Registered: 2006-08-24

Posts: 325

Everybody is the same person - irrefutable proof!

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 of n people are, in fact, the same person.

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Bad speling makes me [sic]

Ninja 101

Member

Registered: 2006-02-20

Posts: 936

Re: Everybody is the same person - irrefutable proof!

WHAAAAAAAAAA??????

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Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized.

coolcat23

Member

Registered: 2006-06-21

Posts: 553

Re: Everybody is the same person - irrefutable proof!

uh..............................

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The world revolves around me. Deal with it.

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: Everybody is the same person - irrefutable proof!

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 of n people are, in fact, the same person.

Very funny.

Nice joke. I like things like this.