one of my friend pointed this out. admittedly it confuses the heck out of me.

2 * 2 = 2+2;
2 * 3 = 2+2+2;
2 * 4 = 2+2+2+2;
...
x * x = x+x+x+....+x+x (x number of times)

x * x =x^2
therefore,
x^2=x+x+x+x+...+x+x (x number of times)
differentiate,
d/dx(x^2)=2x
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (x number of times)
which equals to x

therefore,
2x=x,
2=1


This post has been edited by lin00b: Jul 10 2009, 01:01 PM

mana question??

i think ur logic is flawed

I'm not really any good in maths and very rusty in calculus already, but why would d(x^2)/dx equals to 2x? Shouldn't it be just x?

please point out the flaw

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Added on July 10, 2009, 12:55 pmno question (ok, maybe i mis-named the topic). sorry
just a solution?

This post has been edited by lin00b: Jul 10 2009, 12:55 PM

lin00b: My suspicion is that the mismatch occurs because you sum the x's x times, and that x times summing up of x's will incur a second additional x on the other side, done rigourously [because the number of terms to be summed up isn't a constant number anymore, but varies also according to the number x]

edit: confirmed in wikipedia
http://en.wikipedia.org/wiki/Invalid_proof..._that_2_.3D_1_2

This post has been edited by bgeh: Jul 10 2009, 01:05 PM

numbers never lie to us...


This post has been edited by vivienne85: Jul 10 2009, 01:44 PM

Source: Wikipedia: Invalid Proof

This post has been edited by Thinkingfox: Jul 15 2009, 09:00 PM

I'm following right up to
2x=(1+1+1+...+1)(x+x+x+...+x)

then its again

isnt 2x= x + x ?

ya...

thinkingfox: No, that isn't my answer, because I can't follow his steps to arrive at that solution

lin00b: I'll give it some thought and see if I can arrive at the same answer through another method, but yes some variation of the product rule will probably be needed here (which seems to be what the wikipedia picture thinkingfox pasted put on his post)

What happen to students now days

Never seem understand the fundamental of function x^2 and 2x.

Plot the graph TS and find the real meaning of differentiate w.r.t (x)

Why /k/ always think it is calculus every time there is d()/dx ???

Don't tell me TS is a uni student

These math tricks are not uncommon. No harm in looking at it in thinking over it.

And what does /k/ has to do with this

d/dx(x^2)=2x
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (2x number of times)
which equals to 2x

therefore,
2x=2x,
2=2

why not like this??

2 * 2 = 2+2;
2 * 3 = 2+2+2;
2 * 4 = 2+2+2+2;
...
x * y = x+x+x+....+x+x (y number of times)

since when did x become a constant??? <removed>.jpg

sorry then, lets make it this way:
2 * 2 = 2+2
3 * 3 = 3+3+3
4 * 4 = 4+4+4+4
x * x =x+x+x+...+x (x number of times)

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Added on July 15, 2009, 6:08 pmhow does d[x+x+x+..+x (x times)]/dx = 1+1+1+...+1 (2x times)?

This post has been edited by lin00b: Jul 15 2009, 06:08 PM

Oops.. I'm sorry about that.

d/dx(x^2)=2x
d/dx(x+x+x+...+x+x)=1+1+1+1+...+1+1+1 (2x number of times)

2x because of d/dx(x^2)=2x

d/dx(x^2) = d/dx(x+x+x+...+x+x)

and

2x = 1+1+1+1+...+1+1+1 (2x number of times)