.9999999999..... =2? (Algebra)

[wordcross]

My brother just showed me the "1=2" proof using simple algebra. For those of you who haven't seen it, it goes something like this:

code:

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a=b


a^2=ab


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


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


a+b=b





and since a=b





2b=b


2=1


and as we all know, .99999...=1, so





.99999...=2

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So my question is, why exactly does this work? I know there's the whole divide by zero thing when you cancel out what's been factored, but why does that matter, in this case, when the algebraic representation works out?

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[borschevsky]

[Antrax]

That's true, but in this case the only problem lies when you divide by (a-b), as a=b -> a^2=ab would pass the zero test (it remains true).
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Dread Pirate Westley]

Then you go and subtract b^2 from both sides and get 0=0. You can factor anything out from that: 756*0=12*0. So, I guess that means 756=12.

Although, that's not really necessary. From 1=2, you can prove all integers are equal.

1=2
1+1=2+1
2=3
1=3

n=n+1
n+1=n+1+1
n+1=n+2
n=n+2

(OK, I'm a bit rusty on my proofs: You prove it for a specific case and you prove it for the general case and your done, right?)

[Antrax]

Okay, so what are you saying?
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Legion]

There's also the multiply by zero bit

[The Cruciverbalist]

The implications of this go way beyond mere math. I mean, George W. Bush and Sadaam Hussein are two people, right? So, substituting one for two, that means George W. Bush and Sadaam Hussein are one person! Of course, this also proves John Kerry is Charles Manson, so I probably wouldn't vote for either one of them. (Not that I can vote, since the 2=1 proof clearly shows that I'm the Taco Bell chihuahua.)

[Dread Pirate Westley]

Not really. I mean you're one person (Which means you're two people) and its one dog. Nowhere have we proven people=dogs (although we probably could).

[Hitchhiker]

There was a great proof once, using similar logic, which proved that Donald Rumsfeld is actually a carrot.

[wordcross]

you need a proof for that?

[Jedo the Jedi]

Well no, you could just watch The Apprentice.

[Jedo the Jedi]

Sorry, that's Donald Trump. I read it wrong. But the same is true.

[This message has been edited by Jedo the Jedi (edited 04-26-2004 01:25 AM).]

[Antrax]

Look. There is nothing wrong, mathematically, in writing:
35*0=2*0
It is true. Nowhere in that proof is anyone multiplying by zero. The only problem is when you try to divide by zero, since this means you're multiplying by 0's opposite, which is nonexistent in R, C, or any field I know of.
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Beartalon]

If you're not multiplying by zero, why are you using *0 ? You mean you're only showing the factoring and just not doing the math?

[Antrax]

You have a=b. That means a^2=b^2 (though not the other way around). Since a=b. you get a^2=ab. Nobody, in any point, did anything like:
a=b |*a

Ergo, no multiplication by zero.
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[borschevsky]

[Samadhi]

[Dread Pirate Westley]

a^2-b^2 is zero (As is ab-b^2). So, really, you can't go any further than that point, because there's not much math you can do with 0=0.
You can factor out (a-b) from both sides, but you could just as easily factor out a^171+3b^155-27c^0.5.