dirbax

Thanks DH , what about the new rules of multiplication isn't it a good way to drop out complex numbers ?

and what if we add the rule 0^-1=1 ?

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

For one abs() isn't smooth, at all, neither is ceiling().

True , I am still working on it in order to minimise the number of functions such as ceil and abs which use semantic definition .

Yes but I still should mention them since I am making the basis of DIMD, an other point is trying to avoid semantic presentation of functions such as

this and go for smooth calculations

I am trying to create a new math branch DIMD

Hi , I am working on some math stuff and I need to check some points ,

so are theses formulas correct ?

ISZ(x) : is it 0 ?

isz (x) = cos ( pi * ( (2*ceil( abs(x) ) + 1)) / 2 ) / cos(1)

Ins : Real number x

Out : 1 if x=0 , 0 if x <> 0

---------------------------------------------------------------

SGN(x) : Sign

sgn(x) = abs(x) / ( x + isz(x) )

Ins : Real number x

Out : 1 if x>0 , 0 if x = 0 , -1 if x < 0

more here

Dirbax

thanks