Criticise the following 'proof' that 3=2

x^3 = x*x^2 = x^2 + x^2 + ... + x^2

differentiate both sides
3x^2 = 2x + 2x + 2x + ... + 2x
3x^2 = 2x * x

3x^2 = 2x^2

3 =2

Question

Criticise the following 'proof' that 3=2

x^3 = x*x^2 = x^2 + x^2 + ... + x^2

differentiate both sides
3x^2 = 2x + 2x + 2x + ... + 2x
3x^2 = 2x * x

3x^2 = 2x^2

3 =2

compassionate · Answer

|dw:1418275761233:dw|
If I have 3 apples in one hand, and 2 in the other, then I have more apples in the hand with 3 apples! :)

perl · Answer

thats true :)

compassionate · Answer

You have to think; the proof is semantics. It's the way you look at things.

compassionate · Answer

x*x^2 =/= x^2 + x^2 because that implies 2x^2 = x*x^2

perl · Answer

i wrote
x*x^2 = x^2 + x^2 + ...  + x^2 ,

perl · Answer

there are x terms of x^2

perl · Answer

comp , you are on the right track though

compassionate · Answer

Huh. I am all too tired. I bet @dan815 , @myininaya , @whpalmer4 , @zepdrix  would love to have a crack at this. Also @wio

perl · Answer

or @ganeshie8

ganeshie8 · Answer

I know another flavor of this proof :) 

x^3 = `x`*x^2 = x^2 + x^2 + ... + x^2


here, number of terms on  right hand side depends on x but the proof is treating it as constant. you need to use chain rule for the right hand side while differentiating