33 replies to this topic

[bonanova]

Spoiler for answer the second

Let T be the square root of 2. Consider the infinite continuedexponential, X=T^(T^(T^(T^(T^..... What is X? Well, we clearlyhave X=T^X. X must be 2 because 2=sqrt(2)^2. Also, X must be 4because 4=sqrt(2)^4. Ergo, 2=4. Dividing both sides by 2 gets1=2. QED

This is great - beautiful, even.
Except, the power tower unfortunately does not converge for both cases (for 2, but alas not for 4 as I remember.)
I made a graph of the divergence point sometime back, I will look for it.

When the records are written, however, this def gets Honorable Mention.

[bushindo]

Spoiler for answer the=the second'=second

Let T be the square root of 2. Consider the infinite continuedexponential, X=T^(T^(T^(T^(T^..... What is X? Well, we clearlyhave X=T^X. X must be 2 because 2=sqrt(2)^2. Also, X must be 4because 4=sqrt(2)^4. Ergo, 2=4. Dividing both sides by 2 gets1=2. QED

This is great - beautiful, even.
Except, the power tower unfortunately does not converge for both cases (for 2, but alas not for 4 as I remember.)
I made a graph of the divergence point sometime back, I will look for it.

When the records are written, however, this def gets Honorable Mention.
 
 

Great proof as well. I have no beef with the power tower, but isn't the argument similar to this one

Spoiler for

Let's say that a variable x satisfies the following relationship,

x^2 - 6x + 8 = 0

Since x=2 and x=4 both satisfy the equation, then 2 = 4, or 1=2. It should be easy to find the weak point now.

[bonanova]

Spoiler for answer the third

Start with the trig identitycos(2x)=cos²(x)-sin²(x)re-arrange the equation tocos(2x)+sin²(x)=cos²(x)take square rootssqrt(cos(2x)+sin²(x))=cos(x)divide by sqrt(2) to getsqrt(cos(2x)+sin²(x))/sqrt(2)=cos(x)/sqrt(2)add (3/2) to both sides(3/2)+sqrt(cos(2x)+sin²(x))/sqrt(2)=(3/2)+cos(x)/sqrt(2)evaluate at x=(3*pi/4) to get2=1.Voila!

Ah, the old dazzle 'em with double angles and parentheses ploy!
Remember it well from my college days.
Did you think I would actually evaluate all those functions?
Unfortunately that is unnecessary. It came out wrong by a factor of 4.
While the problem asked for a "proof" that 1=2; you ended up with 2=1; I.e., that 4=2.

In a dyslexic world, where a skeptic is unsure there is such a thing as a dog, that might suffice.
But I'm afraid the quest must go on.

Efforts should be rewarded, nonetheless. Thus, a clue.
If you get far enough out of the box, it might be the start of a relaxing hour after work.

[bonanova]

Spoiler for answer the=the second'=second

Let T be the square root of 2. Consider the infinite continuedexponential, X=T^(T^(T^(T^(T^..... What is X? Well, we clearlyhave X=T^X. X must be 2 because 2=sqrt(2)^2. Also, X must be 4because 4=sqrt(2)^4. Ergo, 2=4. Dividing both sides by 2 gets1=2. QED

This is great - beautiful, even.Except, the power tower unfortunately does not converge for both cases (for 2, but alas not for 4 as I remember.)I made a graph of the divergence point sometime back, I will look for it.When the records are written, however, this def gets Honorable Mention.  

Great proof as well. I have no beef with the power tower, but isn't the argument similar to this one

Spoiler for

Let's say that a variable x satisfies the following relationship,x^2 - 6x + 8 = 0Since x=2 and x=4 both satisfy the equation, then 2 = 4, or 1=2. It should be easy to find the weak point now.

Nicely debunked Bushindo.

However, as I stand now the the company of two great logicians/mathematicians, I tread lightly regarding weak points, knowing the desired solution might likewise be so described. Its redeeming quality being only that it fits the given conditions so nicely.

[bonanova]

Spoiler for Maybe this is it

Write: For x > 0,
x + x + x + ... + x (x terms) = x²

Differentiate with respect to x:
1 + 1 + 1 + ... + 1 (x terms) = 2x
x = 2x.

Divide by x > 0.
1 = 2.

No. Sorry that's not it, either. Keep trying.

[BobbyGo]

Spoiler for

I remember reading somewhere (it might have even been this site, for all I know) that 1 = 2 was used in some kind of physics conversion.  Ohms to amps maybe? Or something close-about?

[CaptainEd]

Yes, but that's physics.

 

My father was a nuclear physicist in the 50's, in the slide rule era. When I was in high school, he explained to me a couple of important principles of applied mathematics:

* For large enough N, anything = 1

* For really large enough N, anything = 0

 

As a corollary, he pointed out (for a different problem than this one), that "2 is one of the larger numbers that is equal to 1".

 

But that's physics...

[bonanova]

Uhhh ... There!  I just cut a king-size hole in the box so we can all leave..

 

Since we're looking for a proof and a symbol, I considered saying what the symbol is.

Suffice it that the symbol would probably bring the search to an end, and specifying the proof most certainly would.

So I'll just let that information itself be the clue.

 

Relax, and let the solution come to you.

[Prime]

I haven't read the entire thread, not sure if someone has not suggested that already.

Spoiler for how about..

(1 - 1.5)² = 0.25
sqrt((1 - 1.5)²)= sqrt(0.25)
1 - 1.5 = 0.5
1 = 2

[TimeSpaceLightForce]

Spoiler for Reciprocity

1 unit = 2 units   vice versa

Time dilation: Special Relativity

A and B are reference frames moving at v m/s.
So that:
A observed (compares) B clock at 1 second
mark while his clock is at 2 seconds mark.
Same is true to:
B observed (compares) A clock at 1 second
mark while his clock is at 2 seconds mark.

Physics are describe by mathematical means
Like Lorentz transformations.