


1 = 2 Proved
#1
Posted 25 April 2006 - 07:34 AM

H tends 2 infinity
---------------------------------
Never argue with an idiot. They drag you down to their level then beat you with experience.
#2
Posted 25 April 2006 - 09:57 AM
Edited by bred, 25 April 2006 - 05:42 PM.
#3
Posted 25 April 2006 - 09:57 AM
Edit: In reply to Bred, no they're not.


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#4
Posted 25 April 2006 - 12:34 PM
#5
Posted 25 April 2006 - 01:16 PM
You are differentiating different equations.
X*X = X

The first is a parabola and the second a straight line.
#6
Posted 25 April 2006 - 02:36 PM
The logic is wrong.
You are differentiating different equations.
X*X = X

The first is a parabola and the second a straight line.
Yes but ultimately it sums up to the same thing, 4^2 = 16 and 4+4+4+4 = 16.
However, yeah they are totally different functions. You would have to use fourier analysis to build two functions from the same building blocks - sine and cosine. Ok maybe I'm over complicating things.
#7
Posted 25 April 2006 - 02:37 PM
tomorrow doesn't matter,
turn that music up,
till the windows start to shatter,
cos you're the only one who can get me on my feet,
& i can't even dance
No Tomorrow - Orson
#8
Posted 25 April 2006 - 04:26 PM
we say x2 = x lots of x
now if we differentiate the entire equation basically its 2x on the left hand side
and on the right hand side every x is 1 aka x lots of 1 which is x
so 2x=x
divide by x
2=1
it "works" because every line makes sense and is mathmatically accurate apart from 2x = x and 2=1 obviously
If i am not here i am somewhere else
#9
Posted 25 April 2006 - 04:35 PM
it "works" because every line makes sense and is mathmatically accurate apart from 2x = x and 2=1 obviously
That's not true - every line appears to make sense! If they were all "mathematically accurate", then by implication 2=1 is mathematically accurate

I've been puzzling over this for a while now - I can think of two ways of stating what is wrong with the "proof", but I'm not completely sure yet. It's actually quite subtle, if I'm thinking on the right lines

#10
Posted 25 April 2006 - 05:11 PM

#11
Posted 25 April 2006 - 07:26 PM

H tends 2 infinity
---------------------------------
Never argue with an idiot. They drag you down to their level then beat you with experience.
#12
Posted 25 April 2006 - 08:26 PM
However, yeah they are totally different functions. You would have to use fourier analysis to build two functions from the same building blocks - sine and cosine. Ok maybe I'm over complicating things.
I guess you've learned about Fourier series recently


#14
Posted 25 April 2006 - 08:39 PM
I'm going for the second line is incorrect, because:

I agree with that; the second line is not an equality.
Now, here are the two thoughts I had:
- The first line is meaningless, because x is not necessarily an integer. (e.g. how can you do
+
+ ... +
"pi times"?)
I'm not really convinced by that though - The "x lots of x" cannot be differentiated termwise, since the number of terms is variable (i.e. there are x terms).
I think that's the best explanation.
#15
Posted 25 April 2006 - 08:45 PM
Party pooper

#16
Posted 25 April 2006 - 08:48 PM
its in the maths textbook. the sign changes when u divide though.
Sorry, but I don't agree (or see where that would happen)!
#17
Posted 25 April 2006 - 10:01 PM
Just that I am enjoying the debate but keeping quiet for now!!

H tends 2 infinity
---------------------------------
Never argue with an idiot. They drag you down to their level then beat you with experience.
#18
Posted 26 April 2006 - 06:36 AM
At X=2
X




Similarly, at X=3, X

Differentiating will give the rate of change (gradient) for each function at a discrete point only.
So, setting d/dx(X


So, 2X = 2 implies that the gradients of both functions = 2 at X = 1.
Similarly, when X = 3, X

ie, gradients = 3 at X = 3/2.
#19
Posted 26 April 2006 - 08:32 AM

As I said previously, the logic is flawed.
At X=2
X




Similarly, at X=3, X

Yes, but if x = 2, then


I don't think this is where the problem is.


If you assume that x takes only positive integer values and differentiate the whole RHS, i.e. taking care of the "x times", then you do not get a contradiction, so this must be where the error is ...
#20
Posted 26 April 2006 - 12:27 PM

They are two different functions which just happen to give the same result at one particular value.
Try thinking of Higher maths questions where a circle and a straight line meet at a tangent; two very different functions but they share one set of values.
Come to think of it, does that mean that a circle is really a straight line?
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