PROOF! That canadians are all the same age

[Defiant]

This ones for you Dan:

All People in Canada are the Same Age
This "proof" will attempt to show that all people in Canada are the same age, by showing by induction that the following
statement (which we'll call "S(n)" for short) is true for all natural numbers n:

Statement S(n): In any group of n people, everyone in that group has the same age.

The conclusion follows from that statement by letting n be the the number of people in Canada.

If you're a little shaky on the principle of induction (which this proof uses), there's a brief summary of it below.

The Fallacious Proof of Statement S(n):

* Step 1: In any group that consists of just one person, everybody in the group has the same age, because after all
there
is only one person!

* Step 2: Therefore, statement S(1) is true.

* Step 3: The next stage in the induction argument is to prove that, whenever S(n) is true for one number (say n=k),
it is also true for the next number (that is, n = k+1).

* Step 4: We can do this by (1) assuming that, in every group of k people, everyone has the same age; then (2)
deducing from it that, in every group of k+1 people, everyone has the same age.

* Step 5: Let G be an arbitrary group of k+1 people; we just need to show that every member of G has the same age.

* Step 6: To do this, we just need to show that, if P and Q are any members of G, then they have the same age.

* Step 7: Consider everybody in G except P. These people form a group of k people, so they must all have the same age
(since we are assuming that, in any group of k people, everyone has the same age).

* Step 8: Consider everybody in G except Q. Again, they form a group of k people, so they must all have the same age.

* Step 9: Let R be someone else in G other than P or Q.

* Step 10: Since Q and R each belong to the group considered in step 7, they are the same age.

* Step 11: Since P and R each belong to the group considered in step 8, they are the same age.

* Step 12: Since Q and R are the same age, and P and R are the same age, it follows that P and Q are the same age.

* Step 13: We have now seen that, if we consider any two people P and Q in G, they have the same age. It follows that
everyone in G has the same age.

* Step 14: The proof is now complete: we have shown that the statement is true for n=1, and we have shown that whenever
it is true for n=k it is also true for n=k+1, so by induction it is true for all n.

[Starbuck]

/\ That is a nice theory

[Oliver]

It is a nice theory, but alas, it is flawed.

You just know this can not be correct so you just have to look for the mastake, that one step that makes everything fall apart. I believe I have found it. Let me try to explain...

I understand your induction theory as it is used often in mathematics. We know for sure that S(1) is correct. Let's assume S(k) is correct also. All we need to do now is prove that S(k+1) is correct. Only then can we say that your statement is true. This can only be achieved when you ADD a new member to the group and prove that your statement is still correct.

What you do is add a new member and take out someone else. Then you say that the new group has k members and therefor it is correct. You need to add a new member and then prove it on that new group. No taking someone else out.

[Defiant]

Leave it to Oli to ruin my anti-canadian fun...

Nice though. I knew there was an error, but of course, I didnt WANT to find it.

[Melodramatic]

how impressive!
Smartie pants..

[GhostOfAMemory]

*goes cross-eyed*

Alrighty then...

*falls over*

[Defiant]

I talked to the friend I got this from. Apparently Oli is completely wrong. This brings me great joy, except that I dont really know.

Apparently the problem is in Step 9.

[Oliver]

[Defiant]

My weak spot is hit. Your anti-proof seems good enough. Personally I hate proofs. I really do. But my friend insists that you are wrong. Oh well, perhaps I can get his ass here, and he can tell you.