Thread: 1 = -1?

What? You've already been given a painstaking explication of exactly this. It isn't a reductio ad absurdum.

The inference from step 3 to step 4 is unfounded. The end.

Originally Posted by Xei

What? You've already been given a painstaking explication of exactly this. It isn't a reductio ad absurdum.

The inference from step 3 to step 4 is unfounded. The end.

With the "painstaking explication," we discussed the legitimacy of squaring the square root of a negative number and getting a negative number. Well, in this proof, the square of sqrt -1 is -1, as you believe it should be. The inference from step 3 to step 4 involves getting the square roots of negatives (not squaring them), which has not been the topic of our discussion. The inference also involves the principle that the square root of a fraction is the square root of the numerator over the square root of the denominator, an issue we have not discussed. So what is the problem in the proof? What exactly goes wrong from step 3 to step 4?