No. The standard field (that is, a ring where both operations are abelian groups) on the complex numbers doesn’t have a multiplicative inverse of 0; rings can’t have a multiplicative inverse for the additive identity. You can create an algebra with a ring as a sub-algebra with such, but it will no longer be a ring. My preferred method is to impose such an algebra on the one-point compactification of the Complex Numbers, where the single added point is denoted as “Ω”.
I started this project when I was 12, and when I could show that the results were self-consistent this was what I had settled on:
let z be a complex number that is not otherwise specified by the following equations. Note: the complex numbers contain the Real numbers, and so the following equations apply to the them as well.
0Ω=Ω0=1
z+Ω=Ω+z=zΩ=Ωz=Ω=ΩΩ
Ω-Ω=0. Ω-Ω=Ω+(-Ω)=Ω+(-1Ω)=Ω+Ω=0
The algebra described above is not associative. That is to say, (AB)C does not always equal A(BC).
If you plot out any number divided by x, as x approaches 0 the answer goes towards Infinity, yes.
When it reaches zero it ceases to be a number.
Every number divided by 0 is “undefined”, and it is not undefined because we can’t describe it, it is undefined because it does not exist, because you cannot divide things by 0.
A number divided by zero equals infinity.
Except if it’s zero then (so 0/0) it is either undefined or any number IIRC.
No. The standard field (that is, a ring where both operations are abelian groups) on the complex numbers doesn’t have a multiplicative inverse of 0; rings can’t have a multiplicative inverse for the additive identity. You can create an algebra with a ring as a sub-algebra with such, but it will no longer be a ring. My preferred method is to impose such an algebra on the one-point compactification of the Complex Numbers, where the single added point is denoted as “Ω”.
I started this project when I was 12, and when I could show that the results were self-consistent this was what I had settled on:
let z be a complex number that is not otherwise specified by the following equations. Note: the complex numbers contain the Real numbers, and so the following equations apply to the them as well.
0Ω=Ω0=1
z+Ω=Ω+z=zΩ=Ωz=Ω=ΩΩ
Ω-Ω=0. Ω-Ω=Ω+(-Ω)=Ω+(-1Ω)=Ω+Ω=0
The algebra described above is not associative. That is to say, (AB)C does not always equal A(BC).
If you plot out any number divided by x, as x approaches 0 the answer goes towards Infinity, yes.
When it reaches zero it ceases to be a number.
Every number divided by 0 is “undefined”, and it is not undefined because we can’t describe it, it is undefined because it does not exist, because you cannot divide things by 0.
Funny that you posted this in a dbzer0.com community (dbzer0 = device by zero).