Cannot be proved.

[Chrissi]

In my geometry & discrete math textbook, there is a sidenote in our proofs unit about a theorem that some dead dude says he proved. The theorem is something along the lines of:

"This theorem cannot be proved."

Huhwhat, you ask? I didn't quite understand at first. What theorem? It took me awhile to understand it was the sentence itself that cannot be proved. But he says he proved it. Huhwhat?

If you try to dig into this, you find that it's a paradox. He says he proved it, but it can't be proved. So he proved that it couldn't be proved? How'd he do that? By not proving it... but if he proved it, the theorem is false! So is the theorem false? No, it can't be proved.

HUHWHAT?

This is the type of stuff that hurts my brain. I haven't looked for this on the internet yet, but here's my theory about how it can be proved.

If you haven't heard of the theory, you needn't worry about whether it can be proven or not. So if he erases his memory.... you get the picture. He can prove it by having never heard of it. Maybe that doesn't make sense. But wouldn't it be damn cool to be able to erase your memory for the sole purpose of proving a theorem that can't be proved?

Okay, seriously.. does this hurt anyone else's brain? I'm feeling it right now.

[perfect_fat]

It's simple.

Everything I say is a lie, except for this sentance.

[VxDx]

well considering the wording should be cannot be proven...I would assume that your book is retarded.

It's possible to prove something cannot be proven, but it's very difficult and only works in specific cases. A bit of a note, there is an idea printed in a math book I read a while back (not a textbook) nobody can prove or disprove the existance of 100 zeros in a row in the decimal notation of PI.

[Ice-Dragon]

The idiocy of what you said hurts my brain... (Chrissi)

[Anonymous]

wow.... perhaps my logic class will have a use after all, and here I thought it was the most worthless thing ever.

Logically speaking, that argument's premises and conclusions are the same statment: "this theorem cannot be proved"

in Truth-Functional-Logic it would look like:

~A .:. A
(read "not-A") (sorry about the extra dot "therefore") ("A")

this statement is a self-contradiction, and therefore is an invalid argument, meaning it holds no value or merit.... but by that same token, since it is invalid, it proves itself at the same time by casual reasoning, therefore it's proven.... in an odd sense.

If it's still bugging you, just be glad you're not a computer and don't have to throw an exception or do a hard-boot to fix the problem. ; )

[peregrine]

above was by me

PS: Synth, if you ever read this, please oh please in the name of whatever gods or magical forces you wish... do something about that logout timer if you can! That or somebody tell me how to disable it if I can. I'll be your best friend!! There's no money involved, but you'll still have that warm and fuzzy feeling from helping somebody!

[Kilgamayan]

[Chrissi]

Ice-Dragon, if you're talking about my second-last paragraph, it wasn't meant to be serious.

Either way this guy proved the theorem can't be proven... mathematically I think. I read something now on the net about how if you add "in axiom system s" to the end and do some weird math... you can prove it. Somehow. I really don't understand it, but the facthat he proved something which cannot be proven is a bit of a "hurting my brain" type thing, for me.

[RobbyZero]

Maybe he was a great mathmatician then and he was on of the best ever to that day and even he could not figure it out so they declared it impossible hhmmm?

[Chrissi]

RobbyZero, you're not serious, are you?

[alainbryden]

It's simple.

Everything I say is a lie, except for this sentance.

That isn't right, that is perfectly possible. The way it goes it

Everything I say is a lie, infact, I am lying, right now.

[RobbyZero]

RobbyZero, you're not serious, are you?

So? Im don't think of this shit on purpose like you do. I don't have time nor the patience to deal with math problems and theorems.

[Chrissi]

All right Robby... calm down, I didn't try to insult you. I just asked a question, and you haven't even answered it yet.

[RobbyZero]

Wow your just like Jam,you interpret stuff the wrong way...pretty sad.


Edit---

ANYWAYS....
You said

In my geometry & discrete math textbook, there is a sidenote in our proofs unit about a theorem that some dead dude says he proved. The theorem is something along the lines of:

"This theorem cannot be proved."

that really doesn't help the situation much for anyone...especially if you don't know anything about that kind of stuff.

But seriously like I said..the guy could be anybody you didn't mention if he was a mathmetician or anything of the sort and that's where I come in.

[Chrissi]

RobbyZero, I don't quite understand what you're trying to say.