Davies Paradox

Davies Paradox

Can you explain this conundrum?

Let us say that:
1
___ = -1
-1

Take the square root of both sides

We have

1^1/2
____ = -1^1/2
-1^1/2

Transposing the denominator from the left side to the right, we have:-

1^1/2 = -1^1/2 X -1^1/2

Rationalizing: 1 = -1 How can this be?


It must be a consequence of the characteristics of -1^1/2 or 'i'



Can it apply to Grapefruits?

Assuming we have a number to represent a grapefruit, G

then

G x 1
_____ = G x -1
-1


Take square roots

G^1/2 x 1^1/2
___________ = G^1/2 x i where -1^1/2 = i
i

As before G^1/2 x 1 = G^1/2 x -1

In fact anything can be operated on by this paradox, including universes (U).

U^1/2 = -U^1/2

or U^1/2 + U^1/2 = 0


For this to be non trivial, ie U =0, then the two U terms must be different.

Help??