Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**Dross****Member**- Registered: 2006-08-24
- Posts: 325

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 ofBad speling makes me [sic]

Offline

**Ninja 101****Member**- Registered: 2006-02-20
- Posts: 936

WHAAAAAAAAAA??????

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

Offline

**coolcat23****Member**- Registered: 2006-06-21
- Posts: 553

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

The world revolves around me. Deal with it.

Offline

**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Dross wrote:

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.

Offline

Pages: **1**