ScaleMaster said:
I am by far no math guru, and I am sorry for bringing up a topic that ended almost 2 months ago, but I just recently discovered this whole "nullity" bs,
The number system he created is perfectly valid. It's his attempts at publicizing it that's junk.
But wouldn't his idea also indicate that numbers have an "end" ?
Kinda sorta. If you take the nonnullity "transreal" numbers, they certainly form a closed interval, [ -\infty, +\infty] with a well-defined first and last element. (Of course, his construction says absolutely nothing about the real numbers)
However, the set of all transreals is not linearly ordered, so I don't think it makes sense to say
that has an end.
Infinity is defined as 1/x as x gets closer and closer to 0
Infinity is defined if and only if you are working in a system that defines it, and it is defined exactly how that system defines it. "1/x as x gets closer and closer to 0" is not a well-formed statement, so I should hope that no system defines infinity in that manner.
I imagine what you
meant to say is that infinity is defined as
\infty := \lim_{x \rightarrow 0} \frac{1}{x}.
That's not how it's
defined in the projective reals, but it's a true statement there. There is no object called "infinity" in the extended reals (though "positive infinity" is often called "infinity" as shorthand). In fact, that limit does not exist in the extended reals: it has both +\infty and -\infty as limit points.
And, of course, this limit doesn't exist in the reals.
he is going off the concept that 1/0 is infinity and is using it as, "the final number" when infinity is not a number, it's a concept.
To reiterate, infinity is exactly what it's defined to be. For example, there are "extended real numbers" named +\infty and -\infty, and there is a "projective real number" named \infty.