Dubious Derivative

**ThePerfectHacker** · January 10th 2006, 02:54 PM

If you can spot the error please do not post the explanation let other people have fun solving it. For the first few days. If you do and I see it I will delete it.

Notice that $x^2=x+x+x...+x$ where $x$ appears $x$ times. Thus, taking the derivative of both sides,
$2x=1+1+1...+1$ but 1 appears $x$ times thus, $2x=x$ ? What is wrong?

**TD!** · January 11th 2006, 04:40 AM

My lips are sealed, unless we're allowed to post our guess in a 'spoiler' kind of tag? Unvisible unless selected.

Perhaps another one, spot the error but don't reveal (or reveal covered using white text in a code box for example).

$e^{2\pi i} = 1 \Leftrightarrow \ln e^{2\pi i} = \ln 1 \Leftrightarrow 2\pi i = 0$

**ThePerfectHacker** · January 11th 2006, 02:32 PM

TD! Your problem is connected with my "paradox" I posed here before.

How did you like the derivative problem?

**Treadstone 71** · January 11th 2006, 05:50 PM

What's the background color used by these boards? We can use it as invisible ink.

**ThePerfectHacker** · January 11th 2006, 06:31 PM

Originally Posted by Treadstone 71

What's the background color used by these boards? We can use it as invisible ink.

I do not know exactly but you can use MS-Paint. They have a color-picker. It is a tools which shows your EXACTLY which color something is.

**CaptainBlack** · January 11th 2006, 09:05 PM

Originally Posted by ThePerfectHacker

I do not know exactly but you can use MS-Paint. They have a color-picker. It is a tools which shows your EXACTLY which color something is.

RGB values 245,245,255 apparently.

RonL

**TD!** · January 12th 2006, 04:04 AM

Originally Posted by ThePerfectHacker

TD! Your problem is connected with my "paradox" I posed here before.

How did you like the derivative problem?

Indeed!

I've seen the derivative fallacy before

**Treadstone 71** · January 12th 2006, 05:06 AM

Hex values are F5F5FF. Click on "quote" to see the exact tags.

**MathGuru** · January 12th 2006, 07:46 AM

If you right in white then [you can barely see it] unless you highlight between the brackets.

**topsquark** · February 15th 2006, 03:32 PM

I'll have to remember this as an annoying "proof" of 2=1. I like it!

-Dan

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