Subject: calculus

Name: sporky
Who is asking: Student
Level: Secondary

Question: Why does the proof for 1=2 not work?

x = 1
x² = 1
x = x²
1 = 2x (derivitive)
1 = 2(1)
1 = 2 ???
 
please tell me where the false logic is.

Draw a picture showing y = x and y= x².

On the picture, you will see TWO things:

1. at x=1, the two graphs cross.
    
   
2. when they cross, they do NOT have the same tangent line and therefore they do not have the same derivative.

So the "=" in line three is an "=" of points, not of functions or graphs. You do not take the derivative of a point - but of a graph.

It would now be your choice as to WHICH of lines 3 or 4 you wanted to say had the flaw in logic.

The way to test the logic in such a string of equations is to substitute, in each line, and SEE when the statements SWITCH from true to false. Good logic always takes a true statement to a true statement. Anything that takes a true statement to a false statement is bad logic!

Line 3 is written as if you can substitute any value of x. However, it is only true if x= 0 or 1.