Hi friends

I am trying to construct a new number set which dosn't have the problem

of division by zero and the square root of negative value

so here is the basic

All arithmitic rules and notions are the same as those of Reals set

except the following statements

0^2=1

if a and b are positive reals and a*b=c

then

a * -b = c "if a>b"

a * -b = -c "if a<=b"

-a * -b = -c

if a=b^n then Root(a) =b "without absolute value"

The rest is the same as the traditional R set

so as a result we have this solultions for old problems :

SquareRoot(-1)=-1 " since -1 * -1 = -1 "

1/0 = 0

0^0 = 0^(1-1) = 0^1 * 0^-1 = 0 * 0=0

So is there any chance this can be correct or at least can be changed so it respects the norm ?

thanks