Real Fuzzy Math

Polarity, when I use it, means positive or negative.  +1 has positive polarity. -1 has negative polarity.

@Baghdaddy:

“Polarity” in this sense refers to the poles in a graph that has asympotic behavior.  The example of an asymptotic equation, y = 3/(2-x) which has a division by zero at x = 2, gives us a “pole” in the graph at x = 2.  Since division by zero is what has caused that pole and the sign of zero defines which side of the pole you are on, the “polarity of zero” actually has meaning both in the esoteric world of mathematicians and in the nuts and bolts world of us poor engineers who are trying to make things work.

But what you are indicating is that this is different than the polarity associated with nonzero numbers.  Do I understand correctly?

@Jennifer:

Polarity, when I use it, means positive or negative.  +1 has positive polarity. -1 has negative polarity.

And if -0 = +0 = 0, then zero has no polarity.  That’s what I’m saying.  Considering zero as negative or positive for a particular application doesn’t make it polar.

Polarity depends on value, and zero is the absence thereof.

@Jennifer:

Actually, I just started the Tired of Games thread to explain why I’m not bothering posting sources.

And um… that did not work out quite like you intended did it Jen?
http://www.axisandallies.org/forums/index.php?topic=9379.0

Considering the results of SUD’s post (confirmed and backed up with links), I think we now know the reason why you failled to do what Baghdaddy did in posting an alternative discussion/explanaiton beyond the original essay…  because you HAD no other knowledge/understanding to convey besides the cut-and paste article that you originally posted from J J O’Connor and E F Robertson.

@Jermofoot:

Jenn claimed that zero has polarity.  I don’t think she can prove that.  To say that it may be necessary or easier to consider negative zero in some situations, I would entirely agree.  But that is not what she said.  Read the first post.

now now - be nice.
She CAN prove that - she just doesn’t want to.  For you do not have the higher learning that would put you in the same realm to be able to be worthy of the proof.

So BD - zero is assigned a “pole” for convenience then?  A group of people decided that in order to grasp an un-graspable “number” decided to grant zero polarity when it was thought useful? 
i.e.

• how much money do you have in your wallet Tim?
• zero
• well . . . that’s better than NO money . . . at least if you’re an engineer . . . :D

@ncscswitch:

@Jennifer:

Actually, I just started the Tired of Games thread to explain why I’m not bothering posting sources.

And um… that did not work out quite like you intended did it Jen?

Whatever.  I don’t need to stoop to your level and give you a free education.  I have more important things to do with my time, like earn my paychecks.

I find it humorous that the person who has now twice been nailed for copyright infringement claims they have to “stoop” to my level.

You have thrown out an argument, one apparently that at least 2 serious researchers in Mathematics feel rather strongly about.  You apparently feel strongly enough in support htat you were willing to claim their work as your own.  Based on that level of support for the theory, I would imagine you would be chomping at the bit to advocate the theory.

You threw down the gauntlet.
You B-slapped everyone on this board with your claims of superiority on this subject.
And then you got caught in an act of plagierism.
Now, you can attempt to prove that you were just being lazy by plagerizing (instead of being deceitful) by demonstrating your PERSONAL knowledge of this theory.

We are all ears to see you expound further on this facinating subject of extreme mathematically theory…

Again, I don’t need to stoop to your level, Switch.  You can think of how superior you are or not superior you are all on your own without my putting you in your place.  I just don’t have the time to deal with closed minded individuals who I am not getting paid to deal with or who are not paying me to deal with them.

@Jennifer:

Again, I don’t need to stoop to your level, Switch.  You can think of how superior you are or not superior you are all on your own without my putting you in your place.  I just don’t have the time to deal with closed minded individuals who I am not getting paid to deal with or who are not paying me to deal with them.

So you had the free time before you ripped off other people’s work, but don’t now.  OK.

Baghdaddy, if YOU have anything to add to your discussions on tihs topic, there are some interested folks here (since you seem to have at least a passing udnerstanding of hte concepts being discussed in that sut-and-pasted essay).  We are just looking for something other than some third party’s essay on it, and for someone to be able to answer questions that are asked on the subject instead of saying we are too ignorant to understand the discussion…

Go ahead with your character assassinations, Switch.  I really don’t care.  I have my opinion on you and what you post too, I’m just too mature to post it anymore.

Jennifer is wrong. 0 does not have a sign.

http://en.wikipedia.org/wiki/Sign_function
http://mathworld.wolfram.com/Sign.html

0 is neither positive nor negative.

x -> -0 is nothing more but a bad notation.

@Jennifer:

I’m not going to get into a debate about the function of zero with a man who’s highest level of math was maybe Calculus II.  Sorry.  But you just don’t have the ground work to have the debate.  Come back after you take Multilinear Equations and Logic I and II.

So how about getting into a debate with someone who has taught Multilinear Equations. May I assume you know about the following mathematical concepts:

• Some basic group theory (uniqueness of the neutral element).
• Polynomial rings and quotients over some ideal, especially R[T]/(T^2), the space of dual numbers.
• Complex analysis including the complex plane and its one point compactification, the Riemann sphere.

@rjclayton:

So Meijing, this is nothing but poor notation?

@Baghdaddy:

http://en.wikipedia.org/wiki/%E2%88%920_(number)

Or are you saying in math there is no such thing as -0?

Let me quote this article:
@Wikipedia:

In mathematical terms there is no concept of a negative (or positive) zero, and −0 is identical to, and represented as, 0.

In math there is no difference between 0 and -0.

There are ways to express infinitesimal numbers below or above 0, with nonstandard analysis or dual numbers. But in either case -0 = 0 = +0. The most common way to express an infinitesimal small number below 0 would be 0 - a·dx, which is not equal to -0.

Floating point numbers can only be used for numerical approximations. The plain outcome of some calculation doesn’t mean anything. You have to check your algorithm to determine the error margin. Check (1.0e100 - 1) - (1.0e100) and look at the sign bit of the result. Does it tell you anything about the sign of the real outcome? The floating point “number” “Negative zero” is nothing but a strange consequence of using a sign bit to differentiate between positive and negative numbers. In the case of 0 there is nothing to differentiate between, but the sign bit wont simply go away.

@rjclayton:

So Meijing, this is nothing but poor notation?

I decided to elaborate, why x -> -0 is poor notation.

First let’s see what this notation is supposed to mean.

The limit expresses the behavior of a function as its parameter approaches a given value. The function defined by f(x) = (x*x)/x + 1 is not defined for x=0 but f(x) = x + 1 for any other value of x. If x is close to 0, f(x) = x + 1 is close to 1. This behavior is written as f(x) -> 1 for x -> 0 or lim(x -> 0)f(x) = 1.

As an other example we will pick the sign function, which is defined by
sign(x) = -1 if x is negative
sign(x) = +1 if x is positive
sign(0) = 0 (which is just mentioned for completeness, but isn’t relevant in this context)

In this case there is no definite behavior for values close to 0. For any x (not equal to 0), no matter how close it is to 0, sign(x) can be +1 or -1. sign(x) does not approach a definite value.

But if we only consider, such values close to 0, which are smaller than 0. There is a definite behavior. For these values sign(x) = -1. If we consider values close to 0, which are greater than 0, sign(x) = +1. There is some definite behavior of sign around 0, but only if we distinguish between approaching the number from the left and approaching it from the right.

x -> -0 is supposed to mean approach 0 from the left. But this is poor notation, as it not possible to use it for other numbers but 0. x -> -1 doesn’t mean approaching -1 (or 1) from the left, but approaching -1 from any side.

A better notation would be x -> 0-, as this notation can also be used for -1 and +1 (x -> -1- an x -> 1-). There are other notations which are even better but impossible to write using BBCode (I hope this link will continue to work).

@cystic:

• how much money do you have in your wallet Tim?
• zero
• well . . . that’s better than NO money . . . at least if you’re an engineer . . . :D

Being an engineer, I consider math useful when applied.  Otherwise it can stay with the poetry books in the library.

As Meijing as explained, much better that I did, the value here is in describing what happens as a variable approaches zero either from a positive or negative term.

As for what Jen was attempting to plagerize, I will leave her hanging from her own petard.