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12th Archivist
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Did you know that 1 = 2? It's just like how 2 = 3 or 3 = 1 or any number equaling any number. I can prove that 1 = 2. Please observe. You could also leave right now, but I'd much appreciate if you preformed the former.

0 * 1 = 0
0 * 2 = 0

Based on this calculation, you could arguably say that 1 = 2, but it is very unlikely that people would agree with this. Continue observing:

0 * 1 = 0 * 2

This is a simplified version of the previous calculation. While some people may accept this opinion, most others won't. At this point, I will have to prove it the way every mathematician proves theirs.

0/0 * 1 = 0/0 * 2
0/0 * 1 = 0/0 * 2 (Removing the unnecessary clutter)
1 = 2

There. That completely proves that through the use of illegal equations, any ridiculous number theory can be proven. Since I've completely proven that 1 = 2, that means there are 2 universes, to Caravel Forums, 2 Eights, 2 worlds, and 2 myselfs. I wondered where that clone potion went...

That concludes my theory. I assume you guys know by now that I am not seriously advocating that this number theory be considered to be true.

Because it's not.

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04-03-2009 at 07:07 AM
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Banjooie
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 icon Re: 1= 2 (0)  
...

Okay!
04-03-2009 at 08:05 AM
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NiroZ
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I prefer this because somehow it disproves the evil atheists.
04-03-2009 at 09:40 AM
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Mikko
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I am one. The Pope is one. Therefore, the Pope and I are one.
04-03-2009 at 10:26 AM
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zex20913
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Yeah--that's why mathematicians are very careful when they divide by zero. It's not normal--indeterminate.

Calculus offers the first examples I know of where dividing by zero is manageable. If you're not there, you don't get to do that yet.

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04-03-2009 at 01:06 PM
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Pilchard VIII
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 icon Re: 1= 2 (+1)  
zex20913 wrote:
Yeah--that's why mathematicians are very careful when they divide by zero.
Click here to view the secret text
;)

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04-03-2009 at 01:49 PM
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rman
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zex20913 wrote: Yeah--that's why mathematicians are very careful when they divide by zero.
Damn, I was gonna say that!:lol

Zero is actually a very weird number.:D

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04-03-2009 at 03:22 PM
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RoboBob3000
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Hey Pilch. Welcome back. :wave:

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04-03-2009 at 05:05 PM
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Kwakstur
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Heh, this just gave me an idea. Let's use some low level calculus here: Limits!
[Each limit is of the full expression in front of it, not just the first term]

 lim  x = 0
 x->0

 lim  2x = 0
 x->0

 lim   x  =  1
 x->0 2x     2

 lim  2x  =  1
 x->0 2x

 lim  x + 2x = 0
 x->0

 lim   x + 2x =  0
x->0  2x   2x   2x

 lim  lim   x + 2x =  lim   0
x->0 x->0  2x   2x   x->0  2x

3  = 0
2

I know the reason why this proof fails, but it's not as readily apparent in the form that I have written it.

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04-05-2009 at 11:20 PM
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agaricus5
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Kwakstur wrote:
 lim  lim   x + 2x =  lim   0
x->0 x->0  2x   2x   x->0  2x

3  = 0
2

Hmm... Isn't the proof failure merely because as x tends to 0, so too does 2x? Thus, your final statement should have been:

3  = 0
2    0
0/0 is indeterminate (it's not necessarily 0), so it could very well equal 3/2.

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[Last edited by agaricus5 at 04-05-2009 11:32 PM]
04-05-2009 at 11:31 PM
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zwetschenwasser
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 icon Re: 1= 2 (0)  
Calculus? Indeterminate forms and L^Hopital's rule? Sweet!

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04-06-2009 at 12:01 AM
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Dischorran
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What I'd really like to see is the proof for .99999... = 2. :|

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04-06-2009 at 12:25 AM
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Nuntar
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 icon Re: 1= 2 (0)  
By long multiplication, (0.999...)^2 = (0.9 x 0.999...) + (0.09 x 0.999...) etc = 0.8999... + 0.08999... + 0.008999... etc = 0.8 + 0.17 + 0.026 etc = 0.999...

Let a = 0.999...

So we know that a^2 = a

Multiplying by a, a^3 = a^2

Since a^2 = a, a^3 = a

Add (a^2 = a), (a^2 = a) and (a^2 = a^3) to get 3a^2 = 2a + a^3

Rearrange: a^2 - a^3 = 2a - 2a^2

Divide through by a: a - a^2 = 2 - 2a

Factor: a(1 - a) = 2(1 - a)

Divide through by (1 - a): a = 2

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04-06-2009 at 12:48 AM
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Kwakstur
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 icon Re: 1= 2 (0)  
Heh, I know what's wrong with that:
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And the problem with mine... agaricus5 has a decent point, but not entirely correct. You have to realize it's a limit.
0/2x  |  x=0
is indeterminate, but 
 lim  0
x->0 2x
is just 0, because even as 2x gets really small, 0/2x is still 0 as long as x isn't actually 0.

The real issue
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[Last edited by Kwakstur at 04-06-2009 01:18 AM]
04-06-2009 at 01:06 AM
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12th Archivist
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While it can be reinforced with simple arithmetic that 0.999... is equal to 1, I still refuse to believe it. I believe that 0.999... is equal to 0.999...

There should be no explanation as to why that is.

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04-06-2009 at 01:08 AM
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Nuntar
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I have no idea what you're saying. "It can be proved with simple arithmetic, but I don't believe it"? Then do you believe simple arithmetic is incorrect? If arithmetic were incorrect, I could put a penny into my bank account at 0.1% interest and earn a million dollars a day.

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04-06-2009 at 01:16 AM
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TripleM
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Gah, I didn't want to enter this conversation again, but it always annoys me when people say they can prove 0.999... = 1. That's just like saying you can prove that n! = 1*2*3*..*n.

0.999... makes no sense without defining what '...' means. And the definition of ... means that the number equals 1.

(True, the definition of ... usually involves an infinite sum, and then you could 'prove' that infinite sum equals 1, but usually people ignore the definition entirely.)
[Last edited by TripleM at 04-06-2009 01:20 AM]
04-06-2009 at 01:19 AM
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Nuntar
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But I didn't say I could prove it equals 1. I said I could prove it equals 2. Of course, since 1 = 2 ......

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04-06-2009 at 01:21 AM
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Kwakstur
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Nuntar wrote:
I have no idea what you're saying. "It can be proved with simple arithmetic, but I don't believe it"? Then do you believe simple arithmetic is incorrect? If arithmetic were incorrect, I could put a penny into my bank account at 0.1% interest and earn a million dollars a day.
Since you didn't specify a unit per time, I'll assume you meant percent per second (or % Hz).

So... 1 day = 86400s. And according to my calculator...

Whoops, my old calculations were for 1%. They're secreted below.
Click here to view the secret text

Okay, here's the real calculations... here's for 0.1%:

1¢ * 1.001^86400 = 3.1937 x10^37 ¢ = 3.1937 x10^35 $

Not quite as big as 10^370, but it's more than a million. And when compounded continuously, it's even bigger!
 /\ 86400
 |               t
 |    (.01$)1.001  dt = 3.1953 x10^38 $ 
\/ 0


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[Last edited by Kwakstur at 04-06-2009 10:29 PM]
04-06-2009 at 01:22 AM
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Nuntar wrote:
I have no idea what you're saying. "It can be proved with simple arithmetic, but I don't believe it"? Then do you believe simple arithmetic is incorrect? If arithmetic were incorrect, I could put a penny into my bank account at 0.1% interest and earn a million dollars a day.
Whoa! Can you give me the name of your bank?
04-06-2009 at 07:47 AM
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Jatopian
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He was speaking hypothetically, with a known false hypothetical.
Nuntar wrote:
I have no idea what you're saying. "It can be proved with simple arithmetic, but I don't believe it"?
Proofs aren't simple, thank you very much.

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04-06-2009 at 06:01 PM
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Insane
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 icon Re: 1= 2 (0)  
If
  1/9 = 0.111...
  2/9 = 0.222...
  3/9 = 0.333...
  4/9 = 0.444...
  5/9 = 0.555...
  6/9 = 0.666...
  7/9 = 0.777...
  8/9 = 0.888...

then wouldn't
  9/9 = 0.999...
  9/9 = 1
  0.999... = 1

be true?
[Last edited by Insane at 04-08-2009 01:29 PM]
04-08-2009 at 01:28 PM
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Nuntar
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04-08-2009 at 03:02 PM
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lopsidation
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I like this "proof":
-1*-1 = 1*1
(-1)^2 = 1^2
sqrt(-1)^2 = sqrt(1)^2
-1 = 1
It's easy to see where the error is, but not so easy if you obfuscate it with algebra and some such.

Here's a great one using calculus:

The derivative of x^2 is 2x.
But x^2 can also be written x+x+x+x+x... x times.
Taking the derivative of x+x+x+x+x... x times gives 1+1+1+1+1... x times.
1+1+1+1+1... x times is, of course, equal to x.
So the derivative of x^2 is x.
Thus, x=2x.
Letting x=1, this becomes 1=2. QED.

There's a simple explanation for why this doesn't work, but the real reason is much, much deeper.

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04-08-2009 at 05:26 PM
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zex20913
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I like this one--I haven't taken Complex Analysis, but I think there's a specific rule declaring that what I'm about to do shouldn't be done.

sqrt(-1)
=sqrt(-1/1)         =sqrt(1/-1)
=sqrt(-1)/sqrt(1)   =sqrt(1)/sqrt(-1)
=sqrt(-1)           =1/sqrt(-1)
=i                  =-i
i=-i
i=0
sqrt(-1)=0.


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[Last edited by zex20913 at 04-08-2009 06:15 PM : tags]
04-08-2009 at 06:15 PM
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Sillyman
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lopsidation wrote:
I like this "proof":
-1*-1 = 1*1
(-1)^2 = 1^2
sqrt(-1)^2 = sqrt(1)^2
-1 = 1
It's easy to see where the error is, but not so easy if you obfuscate it with algebra and some such.
The error is, of course, the order of operations. You should be taking the square root of (-1^2), not squaring i.

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[Last edited by Sillyman at 04-08-2009 06:24 PM]
04-08-2009 at 06:24 PM
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zex20913
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I'm pretty sure that for something like 8^(2/3), you could do either the squared part or the root part first. Roots are part of the exponent sector.

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04-08-2009 at 06:36 PM
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b0rsuk
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12th Archivist wrote:
While it can be reinforced with simple arithmetic that 0.999... is equal to 1, I still refuse to believe it. I believe that 0.999... is equal to 0.999...

There should be no explanation as to why that is.

Oh come on, mathematical notation is not universal truth or anything. It's a way of describing things.

Show me a photo of -3 cats. Go ahead, just be aware I'll wrap your innards around a tree if any cat gets hurt. And you can't lie to me, I'll look into your eyes and I'll know.

I used to think complex numbers (like pow(i, 2) = -1) were ridiculous, but then I realised something much simpler - negative numbers - is both widely accepted and nonexistant. Yet few have problems imagining uses for negative numbers.

Going further, some people actually rejected euclidean geometry, especially his parallel postulate saying that two parallel lines always remain within the same distance of each other.

Another way to describe the differences between these geometries is as follows: Consider two straight lines indefinitely extended in a two-dimensional plane that are both perpendicular to a third line. In Euclidean geometry the lines remain at a constant distance from each other, and are known as parallels. In hyperbolic geometry they "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels. In elliptic geometry the lines "curve toward" each other and eventually intersect.
http://en.wikipedia.org/wiki/Non-Euclidean_geometry

Non-euclidean geometry was useful for people like Einstein. And from what I've heard on a lecture, it's useful for describing physics inside of a star.

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[Last edited by b0rsuk at 04-12-2009 06:32 AM]
04-12-2009 at 06:32 AM
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Banjooie
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The part that baffles me with these equations is that people remove square roots from both sides.

a^2 = b^2
reduces to +-a = +-b

remember, the square root of four is positive or negative two. :D
04-12-2009 at 06:54 AM
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zex20913
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b0rsuk--Negative numbers weren't widely accepted until later than you'd think by the mathematical community--the 17th century! (Focusing on the European math history--other cultures may have used negative numbers before then...though it's unlikely.) As for the -3 cats, had I 3 cats, I would make them all wear i^2 shirts, and then take a photo. But I have neither the cats nor the desire to get some. Plus, it wouldn't be showing -3, anyway.

Banj--technically, the square root, by itself, is merely the positive. It's defined that way. When we take the square root on both sides, then we must denote the positive and negative root.

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04-12-2009 at 01:43 PM
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