Is that "nullity" theory somewhere officialy published?
On that BBC site there is an answer of that proffesor on many posts that he will provide more proofs soon, which left me with doubt whether he actually did fully define that theory or did he just wanted publicity!
Here is something that would help you understand why division by zero is undefined.
$\displaystyle a/b=ab^{-1}$
Where, $\displaystyle b^{-1}$ is the unique solution to,
$\displaystyle bx=xb=1$.
Where, $\displaystyle 1$ is the unique element such that,
$\displaystyle c1=1c=c$.
Now,
$\displaystyle a/0=a0^{-1}$
Thus, we $\displaystyle 0^{-1}$ is unique solution to,
$\displaystyle 0x=1$.
But, that is not possible.
The reason that is not possible is because,
$\displaystyle 0x=(1-1)x=x-x=0$
Thus any element multiplied with zero is zero.
Thus there is no solution to the equation above.
You seem to be lacking in imagination today.
We would be talking here of another version of the extended reals with
three ideal elements added +inf, -inf, nan. That makes nan an element
of the $\displaystyle \mathbb{S} \rm{uper} \mathbb{E} xtended \mathbb{R} eals^{(tm)}$.
Why are we interested in number at all if not because of its usefullness----
Maybe, what you are saying is useful in computer science. But I do not know.
in games and puzzles?
Also, alarm bells should be sounding in your head as you type that statement.
If it were usefull then maths should look at it as usefull tricks in computation
always should be of interest to maths.
RonL
Such a defintion, is mathematically acceptable.
However, what are the binary operations on this set?*)
I am willing to bet whatever they do not even turn this set into a ring.
*)That is the only thing you must do for me, otherwise, I cannot accept this defintion.**)
**)And if they are none, for these elements. What is even the purpose in defining such elements, it does not even form a monoid! Or whatever you call it.
The operations are +, -, *, / as normal. With:
$\displaystyle
nan \circ x =nan
$
$\displaystyle
x \circ nan =nan
$
for all $\displaystyle x \in \mathbb{SER}$ where $\displaystyle \circ$ denotes
any of the operations.
It's my job here to point out that this might be a structure of interest
not to show what existing type of structure it is.
*)That is the only thing you must do for me, otherwise, I cannot accept this defintion.**)
**)And if they are none, for these elements. What is even the purpose in defining such elements, it does not even form a monoid! Or whatever you call it.
I do not know what you are using, but - and / are not binary operation.
They represent the inverse operation of + and *.
In the way I defined them above.
So I am going to pretend you did not mention the - and / and work with * and +.
You did not define the binary operation between inf and -inf and its elements.
You are assuming this algebra structure (and I believe you are reffering to the Extended Reals) is a ring, that is distribution is true. It does not work anymore.
Furthermore, in what I said, all elements have binary operations with each other. Over here not all do (that is some are not defined). So there is no problem.
I just have to go off in defense of intelligent design really fast:
intl. design is NOT:
1. religous. People in all sorts of religions stand with this theory.
2. philisophical. Intl. design proponents are very careful to attatch no description of what intelligence made us to the theory.
3. unscientific. The theory has come up with a way of quantatively telling whether inteeligence made something or not and many proven scientific theories support, through that method, the idea of intl. design.
Is it right? No one knows for sure. Is evolution right? No one knows that, either.
ANYWAY:
It pains me to think about what the proffesor was doing. He is either really, really out of it or is so egotisical he deserves a world record. Either way, he should be put in a mental hospital .