Clever proofs or bad math?

[FatAlbo]

My physics TA showed these to the class. Along the same lines of the 2=1 proofs. I'm not exactly sure what's wrong with the first one, but I've got an idea for the second. Just curious as to what the math genuises here think.

#1
#2

 

[IcemanJer]

in the first proof he's replacing an imaginary number sqrt(-1) by a real number. These can't be interchanged that easily.

 

[IcemanJer]

for the second one, I know you can't go from step 2 to step 3, although I'm not exactly sure if I can explain it properly.

 

[Dark4ng3l]

well uh the first one is screwed up because i canot equal -1 because it falsifies i^2=-1

 

[notfred]

sqrt(1) is +/- 1, not just 1.

 

[rgwalt]

Originally posted by: notfred
sqrt(1) is +/- 1, not just 1.

Thats the error. sqrt(1) is 1 or -1. The answer in this case is -1 as it validates the equation.

For the second proof, 2x = x only for x = 0, so dividing both sides by x invalidates the equation.

Ryan