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### Topic: what's my mistake?  (Read 8249 times)

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#### Riley_5000

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##### what's my mistake?
« on: October 24, 2008, 05:24:50 AM »
I remember seeing a ln paradoxical proof a while ago. I can't remember it, so I came up with my own (I hope it's not the same!!)

say x =1

ln ((x^-2)/(x^2)) = 0

lnx^-2 - lnx^2 =0

lnx^-2 = lnx^2

-2lnx = 2lnx

-2 = 2

What do you think?

#### azmanam

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##### Re: what's my mistake?
« Reply #1 on: October 24, 2008, 08:46:05 AM »
(x-2/x2) = 1/x4.  It does not equal 1.
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#### P

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##### Re: what's my mistake?
« Reply #2 on: October 24, 2008, 09:19:05 AM »
(x-2/x2) = 1/x4.  It does not equal 1.

does when x = 1 though!
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#### azmanam

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##### Re: what's my mistake?
« Reply #3 on: October 24, 2008, 09:39:43 AM »
...

which is what op stipulated in his first statement...

no math in the morning for me...

carry on.
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#### Yggdrasil

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##### Re: what's my mistake?
« Reply #4 on: October 24, 2008, 06:40:44 PM »
As with all contradictory proofs, it involves division by zero.  ln(x)=ln(1)=0.

#### Borek

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##### Re: what's my mistake?
« Reply #5 on: October 24, 2008, 07:00:17 PM »
As with all contradictory proofs, it involves division by zero.

Not all, I have seen much more subtle one, using complex numbers
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#### Riley_5000

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##### Re: what's my mistake?
« Reply #6 on: October 28, 2008, 01:00:23 AM »
Substitute "n" for "-2"

you get :
-n=n

It doesn't matter what x equals! Why do I do this to myself?

#### Yggdrasil

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##### Re: what's my mistake?
« Reply #7 on: October 28, 2008, 10:11:13 PM »
ln ((x^-2)/(x^2)) = 0 is true only for x=1.

$$log \left( \frac{(1/4)}{4} \right) = log(1/16) \neq 0 /$$

#### vhpk

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##### Re: what's my mistake?
« Reply #8 on: November 16, 2008, 04:54:50 AM »
I remember seeing a ln paradoxical proof a while ago. I can't remember it, so I came up with my own (I hope it's not the same!!)

say x =1

ln ((x^-2)/(x^2)) = 0

lnx^-2 - lnx^2 =0

lnx^-2 = lnx^2

-2lnx = 2lnx

-2 = 2

What do you think?
All of your expression are trues except the final step. Since lnx = 0 as x is equal to 1, you divide lnx for both sides i.e you divide 0 -> that's the mistake you've made.
Good luck
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