Real Fuzzy Math

Higher math explains what exactly is happening with limits of undefined results.  It’s less a matter of undoing the teachings as it is expounding on why you were taught that and how to logically arrive at the answer through other, more accurate means.

@Jennifer:

And in lower level math you can negate the polarity of zero, it actually makes lower level math much simpler and easier for beginning mathematicians to understand.  But just because you ignore something does not mean it does not exist.

I don’t ignore it - there is no polarity of zero.
A car in reverse has a negative velocity, a car in drive has a positive velocity.  A parked car has no velocity (unless you include it’s velocity on the planet).  It has no polarity because it is nothing.  Plain & simple.

For instance, 1/x when x=0 is said to be undefined.  Technically true.  Literally not.  y= infinity and negative infinity at that point and so, since a function cannot have two outputs for one imput, they have to figure out WHY it has two outputs.  The answer?  You had two inputs.  +0 and -0.  But for algebra and trigonometry and calculus I, II and III it’s much simpler to keep the students from being confused and just tell them that the answer is undefined.

f(X) = 1/X IS undefined.  Simply put, X or Y can’t equal zero because 0 /= 1.  There are not two outputs for one input (which IS possible, try f(X) = X2) - just look at the graph!  Zero is absolute - you either have nothing, or you have something.

Jermo, talk to me when you get into higher level math.

This board does not have support for the appropriate symbology for me to demonstrate just how clueless you are when it comes to pure, logical mathematics.  At very low level calculus and low level physics, yes, you may ignore the polarity of zero.  Sometimes logic dictates that zero has no polarity.  Just like sometimes logic dictates your answer to the question of the velocity of a baseball thrown by a man on planet earth.  Obviously that is going to be bound by 0 < X < 300 miles per hour.  So any answer you get over 300 miles per hour just isn’t going to make mathematical sense for THAT problem.  Does that mean 400 miles per hour does not exist?  Of course not!

@Jennifer:

Jermo, talk to me when you get into higher level math.

This board does not have support for the appropriate symbology for me to demonstrate just how clueless you are when it comes to pure, logical mathematics.  At very low level calculus and low level physics, yes, you may ignore the polarity of zero.  Sometimes logic dictates that zero has no polarity.  Just like sometimes logic dictates your answer to the question of the velocity of a baseball thrown by a man on planet earth.  Obviously that is going to be bound by 0 < X < 300 miles per hour.  So any answer you get over 300 miles per hour just isn’t going to make mathematical sense for THAT problem.  Does that mean 400 miles per hour does not exist?  Of course not!

I’m ready to listen, but apparently you aren’t ready to explain it.  What the hell does the baseball velocity have to do with the polarity of zero?
Here’s a fun one for ya, Jen.
A negative times a negative = a positive
A positive times a positive = a positive
A negative times a positive = a negative
A positive or negative times zero = ?
What is it Jen?  I can guarantee you that even if a “positive” or “negative” zero exists, the answer is still the same.

Depends on the rest of the question.  Are you ONLY talking about +0 and -0?

Which is first?  -0 or +0?  Yes it makes a difference.  I won’t answer until you tell me WHY it makes a difference.  I get paid GOOD money for this information, so I don’t want to give it free to a person who either won’t understand it or won’t appreciate it.

@Jennifer:

Depends on the rest of the question.  Are you ONLY talking about +0 and -0?

I’m not indicating that there is a positive or negative 0.

Which is first?  -0 or +0?  Yes it makes a difference.  I won’t answer until you tell me WHY it makes a difference.  I get paid GOOD money for this information, so I don’t want to give it free to a person who either won’t understand it or won’t appreciate it.

Fine.  You can be stubborn if you want.  I’m waiting for proof of your claim of a polar zero.  I still deny it.  And until you show proof - which I doubt you will - I will remain unconvinced.  I won’t hold my breath though.

I cited sources.  If that’s not good enough for you, then tough tiddlywinks.  The mathematical community has come to “consensus” that there is polarity on zero.

You catch more flies with honey than vinegar, Jen.

You don’t do yourself much service by telling everyone how much more advanced you are in Math than them, then refusing to even try to explain a concept to willing listeners who don’t understand how you are correct. And citing sources is even worse, because if its such advanced math, they have less chance of understanding it in a textbook then from another who understands it and can explain things to them.

Don’t explain it if you don’t want, but you come off as an arrogant jerk, IMO.

I tried to simplify it so most people could understand it.  I don’t really get into theoretical mathematics for that reason.  At least not on this board.  But after you put forth sources and one person continually demands sources from you on the same thread, same topic, you just get to the point of not caring.

I’m not saying he’s an ignoramous.  I’m just saying he has not dedicated years of his life and tens of thousands of dollars to the study of high level mathematical equations and functions.  How am I supposed to have a high level discussion about it with him?  I tried to make it a lower level discussion, but when you do that, you do lose a lot in transition.  Though, I made a valiant attempt.  It’s just difficult when people have been telling you something completely different so as not to confuse you and then have someone present the facts without the blinders placed on them.

Anyway, a three year story turned into one line:

Zero has polarity.  This polarity is normally so trivial as to be ignored in 99.9% of the instances zero appears (or more.)  However, just because it’s trivial does not mean it does not exist.

@Jennifer:

I tried to simplify it so most people could understand it.  I don’t really get into theoretical mathematics for that reason.  At least not on this board.  But after you put forth sources and one person continually demands sources from you on the same thread, same topic, you just get to the point of not caring.

I’m not saying he’s an ignoramous.  I’m just saying he has not dedicated years of his life and tens of thousands of dollars to the study of high level mathematical equations and functions.  How am I supposed to have a high level discussion about it with him?  I tried to make it a lower level discussion, but when you do that, you do lose a lot in transition.  Though, I made a valiant attempt.  It’s just difficult when people have been telling you something completely different so as not to confuse you and then have someone present the facts without the blinders placed on them.

Anyway, a three year story turned into one line:

Zero has polarity.  This polarity is normally so trivial as to be ignored in 99.9% of the instances zero appears (or more.)  However, just because it’s trivial does not mean it does not exist.

Well, you didn’t exactly try to explain.  You talked about other things.  So, I went looking myself.

http://en.wikipedia.org/wiki/Negative_zero

−0 is the representation of negative zero or minus zero, a number that exists in computing, in some signed number representations for integers, and in most floating point number representations. In mathematical terms there is no concept of a negative (or positive) zero, and −0 is identical to, and represented as, 0. In science, −0 may be used to denote a quantity which is less than zero, but which is too small in magnitude to be rounded down to −1. In statistical mechanics, certain systems in a state of population inversion may be considered to have an absolute temperature of −0.

I don’t see anything that matches what you have said, Jenn.

As I said, I’m not debating it further until you can prove up with some higher level math.  Until then, I don’t believe you’d understand the terms I’d need to go into more depth.  Not saying you are not intelligent, just that you have not been exposed to the subject matter at hand.

@Jennifer:

As I said, I’m not debating it further until you can prove up with some higher level math.  Until then, I don’t believe you’d understand the terms I’d need to go into more depth.  Not saying you are not intelligent, just that you have not been exposed to the subject matter at hand.

Too late, I found my answer.  Have fun with your voodoo.

Dunno what reprint you have, I’m looking at mine right now and using it for a proof.

Ouch…

Same ISBN number, same source.  Disparate answers…

I guess that those of us reading along at home are left with trying to determine which of the two posters is more believable… unless we also go out an buy this particular book (since no one has posted a free online source… other than sources that show zero as non-negative  :mrgreen:)

I can admit when I’m wrong.  I just need some evidence showing it.  I think everyone here has been gracious enough to afford Jenn ANOTHER chance to prove her claims.  It’s not asking much.  It’s a learning experience for everyone.

Anyway, I knew we had another discussion about a claim Jenn made concerning zero, and finally tracked it down.  It starts here and goes for a while without conclusion (dividing by zero):

http://www.axisandallies.org/forums/index.php?topic=7456.60

Actually, I see it’s about research into the possibility of dividing zero.  All I’ve got to say, why is Jenn obsessed with zero???

Assigning a polarity to zero is an accepted practice that allows otherwise insolvable problems to become tractable.

Jenn has guided the readers of this thread in that direction and she is correct in what she has said so far.  She is also correct in that this is a concept that is much easier to handle when Multi-variable Calculus is part of your routine mathematical tool box.

“BALDERDASH!!!” you say?

First we can start with how it is represented.
http://en.wikipedia.org/wiki/−0_(number)#Representations
I think it is worth noting that the concept of negative zero is useful enough that is is defined in 1+7 bit sign-and-magnitude representation, simple binary, one’s complement, and the IEEE 754 standard.   Jenn is not alone in her interest (fascination?) with signed zero.

“I don’t care that you can write negative zero, what is it’s value?”
http://en.wikipedia.org/wiki/−0_(number)#Properties_and_handling
As the link describes, there are various means of comparing (-0), (0) and (+0) and getting a value ranking and different answers that are useful.

“All very interesting but what is it good for?”
http://en.wikipedia.org/wiki/−0_(number)#Scientific_uses
This is a fairly simple case where the idea of negative zero is used to describe days where the temperature is below 0 but not -1.Â

More complex examples are available but to be bluntly truthful about it, with out that multi-variable calculus background that I mentioned and an abiding interest in the topic, your eyes will glaze over.

“But I really want to know!!!”

Good for you.

Lets put together a very simple control system.  We have a submarine with a compass and a rudder.  We tell it to steer a course using the rudder.  If the submarine points to the left of the ordered course we have the control system provide right rudder to return it toward the ordered course.  We do the opposite if the submarine points to the right of ordered course.  This gets expressed mathematically as “Rudder Angle = (Ordered course - Actual course)” where positive values for Rudder Angle correspond to right rudder.  This works great if the ordered course is 180 and the actual course is 175.  We get 5 degrees of right rudder.  As long as the control loop is faster than the response time of the vehicle this will bring the vehicle back to the ordered course.

Now lets put some stress on our control system.  Ordered course is 358.  Actual course is 002.  our rudder angle is now = +356 but this value takes us the long way around to the desired course instead of a negative (left) rudder taking us back to the ordered course the short way.  The end result is your control system occasionally has the vehicle do right hand cirlces if it gets knocked off course too far.  In addition, the controller attempted to drive the rudder to an angle that it could not reach.  This is not desirable.

In order to avoid these kinds of issues we start to do things like take derivates and integrands of actual and ordered courses.  From this we develop orders for the rudder.

http://en.wikipedia.org/wiki/Derivative
http://en.wikipedia.org/wiki/Integral

Sadly, as nice as these tools are for smoothing the wild swings of the rudder, we know have to deal with mathematical functions that will give us zeros at awkward times.  Even more confusing is we also have to take into account the performance of the vehicle at different speeds, environments and configurations.

Remember the idea that the control loop needs to be faster than the vehicle response?  There is a lot more mathematics behind that statement than I care to type.  The end result is asymptotic behaviours.  This means we need to know what the “sign” is of zero as we approach that asymptotic point in the control system.

Confused yet?

If not, consider a career in engineering.  If you are confused, don’t feel bad. I probably totally goofed on the explanation somewhere.

Jen- are you taking notes? Thats what everyone was looking for from you when they asked you to explain it. Not “you need more higher level math” or citations to some print essay that would explain nothing to the average reader anyway- just an earnest attempt to explain the concept. Even if people come away now still unsure, they know that Baghdaddy tried to explain it, and posted links to web resources for further info.

Again- no one was saying you were wrong and that they knew more then you, they were saying that your claims contradicted what knowledge of the subject they had, and wanted an explanation of why/how you were right. You don’t have to teach them entire fields of mathematics, just make some attempt to give them a basic understanding of the concept of negative and positive zero since everything they knew till that point said zero is not negative.