# New number set

• March 15th, 2009, 10:12 PM
dirbax
New number set
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
• March 15th, 2009, 11:08 PM
MagiMaster
Well, I see two things wrong with your current line of thinking.

Mainly, you seem to be operating under the misconception that there's a problem with division by zero and imaginary numbers. That said, it can be fun to try and work out new stuff. Just don't be surprised if it doesn't work out perfectly.

Other than that, your definition of multiplication is not continuous. I think this would lead to some serious problems, but I can't be absolutely sure right off hand. Anyway, to make sure that your structure can do at least some of what the real numbers can do, you should make sure it conforms to the field axioms.
• March 16th, 2009, 12:08 AM
dirbax
Hi magimaster what does it mean " definition of multiplication is not continuous" ?

and what if we add the rule 0^-1=1 ?
• March 17th, 2009, 06:23 PM
Manynames
Re: New number set
Quote:

Originally Posted by dirbax if and are positive reals and then "if " "if "
-a * -b = -c
if then "without absolute value"

The rest is the same as the traditional R set

so as a result we have this solultions for old problems : " since "  So is there any chance this can be correct or at least can be changed so it respects the norm ?

thanks

It's much more pleasurable with latex. As shown.

You seem to be under the contention that there is an anvalidity to division with zero's, which would be my main point by the way.
• March 17th, 2009, 07:20 PM
Numsgil
How much background do you have in advanced mathematics? We did some stuff like this as part of a class I took in college. Abstract algebra maybe? Anyway, there's a whole bunch of formal rules you can use to examine what you've constructed and see any problems it will have. But it's been years and I don't remember them :)