The Nullity

Originally posted by uzless
we had a similar debate here just after I signed up last year. I forget the thread but I remember I was roundly thrashed for suggesting something similar to what this guy has done.

Anyone remember the thread?

Of course I do, I started it. It was about e^pi(i) + 1 = 0.

There seems to be no problem with what this person has done except that the whole idea seems trivial. The operation 0/0 has already been defined in numerous ways and unlike i, which can be manipulated in equations and has concrete effects on mathematics, this "nullity," when introduced is impossible to remove. Nullity and any operation equals nullity.

That anyway, is how it appears to me. But perhaps I am missing something. Which is why I started this thread.

Originally posted by genius
is 0^0 not 1?

if 0/0=nullity, what would that mean for when you are posed with finding the limit of a sequence which involves dividing by zero?

for instance, lim(x->0) of sin(x)/x = lim(x->0)cos(x)/1=1 (by l'hopitals rule), but it also equals the nullity. or am i just confused? i don't have time to look at this properly, but i'll read the paper sometime...maybe...it sounds...interesting...

The division '0/0' in the l'Hôpitals rule is never actually perfomed. It is used only as a limit, nothing else. Therefore the nullity concept is never used here.

If one actually do the 0/0 division one came to on result one time and onother result another time. Therefore one nullity doesn't equal another nullity. So the nullity can't be defined as a number in any number system, invented or not yet invented.

Even if you define 0/0 as q, what happens with addition? Is q+q equals 2q? Does q*q equals q^2? What happens if you divide 1 with q? Does (1/q)*q equal q again?

And the last question - what can you use this nullity for? Is it of any mathematical value?

Or is it just a funny thing to discuss, nothing else?

Originally posted by FabianFnas
The division '0/0' in the l'Hôpitals rule is never actually perfomed. It is used only as a limit, nothing else. Therefore the nullity concept is never used here.

If one actually do the 0/0 division one came to on result one time and onother result another time. Therefore one nullity doesn't equal another nullity. So the nullity can't be defined as a nu ...[text shortened]... ? Is it of any mathematical value?

Or is it just a funny thing to discuss, nothing else?

"To be quite precise: I am saying that the number 0/0 is a number. It is a fixed number, not an undefined number or anything like that. That is different to what goes on currently in computing, and in mathematics....NaN is, as it says, not a number. Nullity is a number - that makes a difference. It is a paradigm shift in the way you think. If you think of 0/0 as a fixed number it changes the way that you do calculus."

http://www.bbc.co.uk/berkshire/content/articles/2006/12/12/nullity_061212_feature.shtml

Originally posted by genius
"To be quite precise: I am saying that the number 0/0 is a number. It is a fixed number, not an undefined number or anything like that. That is different to what goes on currently in computing, and in mathematics....NaN is, as it says, not a number. Nullity is a number - that makes a difference. It is a paradigm shift in the way you think. If you think of 0/0 ...[text shortened]... s."

http://www.bbc.co.uk/berkshire/content/articles/2006/12/12/nullity_061212_feature.shtml

...and there are people that believe in perpetuum mobile too. With equally vague explanation...

Originally posted by FabianFnas
...and there are people that believe in perpetuum mobile too. With equally vague explanation...

no no no! he was precise! he even said so...!