Question

The following is my attempt at proving that 1<-1 . In which of these steps did I first make a mistake?
Step 1: Let i = sqrt(-1) then i^2 = -1 and i^4=1.
Step 2: Hence, we have i^2 < i^4
Step 3: We divide both sides by i to get i < i^3.
Step 4: We divide both sides by i again to get 1<i^2 or 1 < -1

Answer 1

With 2 subsequent divisions by 'i',
you are effectively diving by i^2 which is -1, a negative quantity.

And we all know, while dividing by negative quantity, the inequality sign should be flipped.

So, finally we get 1 >-1 which is true.