Let us suppose, that we have three numbers - A, B and C.

Let us suppose, that A + B = C

A^2 - B^2 = (A - B) * (A + B)

A^2 - B^2 = (A - B) * C

A^2 - B^2 = AC - BC

A^2 - AC = B^2 - BC

A^2 - AC + AB = B^2 - BC + AB

A(A - C + B) = B (B - C + A)

Now, obviously, A - C + B = B - C + A, so let`s divide both sides on it.

A = B


Comments, anyone?
(Yes, it`s obviously sofism. Can you guess, where the wanky part is?)

A - C + B = B - C + A = 0. Divide by 0 = universe explodes.

Edit: I don't understand what you mean by Sofism is a weird spelling of Sufism, which is a mystic Islamic tradition that held that all deities were different manifestations of the one God Allah, and stressed spiritual connection with that entity and became popular with the common people because it was more lax than strict Islam and involved stuff like dancing.

Edit 2: Nvm, did you mean "a sophism"?

Edit 3: spoilerized it

Good call. ^_^

Can you hide the answer for now, though? I`m wondering, how people will respond.

You're dividing by zero. (A - C + B)

Yes. Sophism. I somertimes mix up ph and f in rare words (Russian has one letter for this sound, not two.).

And it's not sophism. Sophism is when you use arguments that make you sound right, even though the argument itself is false or flawed. To quote wikipedia "rhetoric that is designed to appeal to the listener on grounds other than the strict logical cogency of the statements being made."

The proof fails for completely different reasons.

....

This proof suggests "logical" proof, that is really based on an illegal operation.

If that does not fills out definition for "sophism", I`d love to hear one of yours.

Yup. What was the point again?

Okay, my definition for sophism is "rhetoric that is designed to appeal to the listener on grounds other than the strict logical cogency of the statements being made."

I don't think an illegal operation is something that appeals to a listener on grounds other than logical cogency. What is going on in this proof is that it appears to be logically coherent, but actually is not. There is no appeal to the readers emotions or sense of humour or anything.

This is sophistry:
[quote=Thank You For Smoking]
Joey Naylor: Mom, why can't I go to California?
Jill Naylor: Because, California's just not a safe place. And besides, I'm not sure it's appropriate for your father to bring you on a business trip.
Joey Naylor: Appropriate for who?
Jill Naylor: What?
Joey Naylor: Mom, is it possible that you're taking the frustration of your failed marriage out on me?
Jill Naylor: Excuse me?
Joey Naylor: This California trip seems like a great learning opportunity and a chance for me to get to know my father. But if you think it's more important to use me to channel your frustration against the man you no longer love I'll understand. [/quote]

There is appeal to logic, which qualifies as well. Check mathematical sophisms. I doubt you`ll find one, that`ll pull tricks like - "Hey, bud, don`t you believe me? Well, I swear to Jeebus and Virgin Mary, that it`s all truth, to the last word!"
(P.S. Strictly speaking, this is not a sophism at all, that`s just mollycoddling.)

Are you saying you doubt that I'll find any mathematical sophisms? (I didn't) Is that because they don't exist?

And appealing to logic is not sophism. Sophism is pretending to appeal to logic while actually appealing to something else, like emotion. This proof is appealing to logic and fails to satisfy it.

Sigh.

Yes, mathematical sophisms exist. Just type "math sophism" in Google, and read up. In fact, first link links to one of the most famous ones. Achilles and turtle.

Achilles runs ten times faster, then turtle.

Let`s assume, that Achilles is hundred steps behind the turtle.

While he runs through this hundred, turtle will move ten steps forward.

While Achilles runs through those ten steps, turtle will move one step forward.

While Achilles will run that one step, turtle will move one tenth of step forward...

Ad Infinutum.

Therefore, Achilles will always close up on turtle, but will never quite outrun the turtle.

Achilles can't run. He has an arrow in his heel.

Ah yes, one of Zeno's paradoxes. Probably everybody who has studied calculus knows this one.

You would have to be pretty dumb to fall for this

Aw crap, maybe you're right.

Maybe.

In any case, sophisms are quite amusing. They demonstrate the "inertia" of thinking process. Very amusing... Especially, if you got caught first.

Here`s a philosophical one...

If halves are equal, then wholes should be equal too...

Half-empty equals half-full, therefore, empty equals full.

Nope. I was wrong. You're abusing the term "sophism". You're saying that any bad logic is sophistry, which is not true. It's only sophistry when you base a debate on something other than logic while maintaining the appearance of logical discourse.

But I'm not going to argue it anymore because it's pointless.

Well, as I said... Let the Google set us apart. I searched for "math sophism" - and first link was Achilles and turtle.

Common consensus seems to agree with this.

On other hand, if you feel like defining "sophism" some other way, feel free to. Just be sure to state it beforehand, to omit the misunderstandings.

Oops. Dictionary.com says that sophism, while also having my definition, is any fallacy.

Damn you dictionary! :angry:

Heh. Don`t worry. Your definition is also correct, so no harm done.

Anyone else here thinking that 90% of posts on this forum belong to Alice Shade?

Damn.

For our name is legion, and we are many.

Jokes aside, it`s Sunday, and I have absolutely nothing better to do. Can`t even go out - girlfriend`s over at her parents` place, and they hate my guts. ^_^

I'm just saying. You got more than 150 posts and 2 threads in less than 2 days.

That must be a record or something.

Well, consider, that most of them are on argument threads. Outside of that, it`d be much more reasonable.

Besides, I just like to talk. ^_^

I used to use this to confuse the hell out of people all the time. I typically used 4 and 5 for the numbers. If you start using large numbers, or numbers separated by a larger range, it starts to get really messy.

Digits work just fine for the purpose, I`d say.

Thank You For Smoking is probably one of the greatest movies ever. Just saying.

No that's not philosophical, it's just wrong. As is the divide by zero trick in your first proof. Just stick some numbers in and watch it fall over.

That`s why they are sophisms, no?

Here's one: You rejecting solid mathematical proofs just because you don't understand them.

Oh, that`s not sophism. That`s slander.

Definitions of sophism on the Web:

a deliberately invalid argument displaying ingenuity in reasoning in the hope of deceiving someone
wordnet.princeton.edu/perl/webwn


And this is why they are not. They were clumsy at best.

Yet, you will find them among the classic mathematical sophisms.

Once again - type "math sophism" in Google, and hit search. First page descibes the sophism with Achilles.

Just because you find that on Google doesn't change the fact that they aren't clever.

Just because there are grammatical rules, it doesn`t makes them logical, then.

Decide on something. Either you blindly follow authority, and thus my english is wrong, and those are legitimate sophisms, either not - thus my english is right for me, and those are not sophisms for you.

Guys, I found a sophism!

.

One of those too, yeah.