Breaking the integrity with differentiation
Emma followed the steps below , and ended up with an unacceptable solution.
Step 1: x^{2}=x * x (x times x)
Step 2: x^{2}=x+x+x+... (x added x times)
Step 3: (taking the derivative of both sides) 2x = 1+1+1+..... (1 added x times )
Step 4: 2x=x
Step 5: 2=1
Which first step in the sequence led to the unacceptable result.
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1 solution
Answer: Step 2 x^{2}=x+x+x+... (x added x times) is valid only for natural values of x. The statement (2.5)^{2}=2.5 added 2.5 times,, has no meaning as any thing added 2.5 times doesn't make any sense.
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