Two funny (but unrelated) proofs

[simX]

OK, I saw this first proof on the EV Nova boards a while ago, but I thought it'd be funny if I posted it here. Remember that this represents the views of one of the people on the EV Nova web boards, not MY views.



OK, and the second proof is that are number system is totally messed up. Here's the proof:

First, say we have two numbers a & b, and they are equal. Thus:

a=b

Multiply by a.

a^2 = ab

Subtract b^2.

a^2 - b^2 = ab - b^2

Factor.

(a+b)(a-b) = b(a-b)

Cancel the (a-b) factors.

a + b = b

Remember that a=b, thus we get

b + b = b

Group like terms.

2b = b

Divide by b.

2 = 1

Scary, huh? A corollary is that if two numbers are equal, both equal 0. Just go from

a + b = b

to

a = 0

by subtracting both sides by b.

Discuss.

[dricci]

Makes me wish I would have paid attention in Algebra!

[nkuvu]

So you want me to shoot the holes in this proof, or does everyone already know them?

[xoot]

LOL! I like the first proof best!

Second Proof: The number system is indeed messed up. I dunno what to say about this, except that you should show someone who is a professor this proof.

[nkuvu]

Sorry -- gotta kill this...

a=b

Multiply by a.

a^2 = ab

Subtract b^2.

a^2 - b^2 = ab - b^2

a = b

So when you multiply by a you get

a^2 = ab

but substitute a back in for b.

a^2 = a^2

subtract b^2 (which is really a^2)

a^2 - b^2 = a^2 - b^2

since b^2 = a^2 you get

0 = 0

end of faulty proof.

[googolplex]

nkuvu is right tricky.

[googolplex]

I just read the first one now. I've seen that somewhere before, Its funnier written down though

[simX]

Originally posted by nkuvu
Sorry -- gotta kill this...

a = b

So when you multiply by a you get

a^2 = ab

but substitute a back in for b.

a^2 = a^2

subtract b^2 (which is really a^2)

a^2 - b^2 = a^2 - b^2

since b^2 = a^2 you get

0 = 0

end of faulty proof.

Um, no. You can't disprove a proof by providing an alternate ending! Where did YOU learn algebra?

Seriously, though, you can't disprove something like that. You have to find fault with the specific steps that I did.

Think of it this way, say I take 3 pencils and arrange them in the form of the letter A. Then you take them and arrange them in the form of the letter N. You can't say, "It's impossible to arrange them like an A, because one can arrange them like an N!"

Basically what your proof said is that 0 = 0. Of course! We all know that. My proof is much more interesting; 2 = 1, which we didn't all know.