[subversion]

Originally Posted by <<>> 0/0 is considered in undefined in mathematics

Actually this is not quite correct either. 0/0 is considered indeterminate, which means it can be shown to be equal to any value.

[hanzoganz]

Originally Posted by subversion Actually this is not quite correct either. 0/0 is considered indeterminate, which means it can be shown to be equal to any value.

Let`s see the classical high school example:

We know that 3x2=6, so 3=6/2

Now, if we try to use cero as a regular number we would have:

5x0=0, so 5= 0/0, which is not that bad but

6x0=0 and 6=0/0 and, by reflection we know that the equallity is commutative so 0/0=6.

We have
5= 0/0
0/0=6

applying transitivite we would conclude that 5=6, wich we know is false.

That`s why dividing by cero is undetermined. Let`s remember that math is based in a set of axioms that, conected, have to be ruled by certain logic.
We invent but not at will.

regards,

or

[subversion]

Originally Posted by hanzoganz That`s why dividing by cero is undetermined. or

But what about when it's undefined? Are you saying that undefined is just a special case of undetermined? How do you know that undetermined isn't a special case of undefined? Or is your above statement not necessarily true because undefined and indeterminate are two completely different things?

[hanzoganz]

Originally Posted by subversion But what about when it's undefined? Are you saying that undefined is just a special case of undetermined? How do you know that undetermined isn't a special case of undefined? Or is your above statement not necessarily true because undefined and indeterminate are two completely different things?

I think the division by cero is pretty clear, isn´t it? Now we have come to a linüistic cundrum: undefined or undetermined. And now, it makes me wonder. Undefined: We say something is not defined when there is no way you can do it. For example, the functions. Lets say square root of -1 is not defined for the Domain of negative real numbers. So, undefined means there is no way to do that calculation in that given systems. Now Undetermined: There is no way to know if something is tru or false. This has to do more with the value of a certain result than the operation itself. The result of the square root of -1 is undetermined ´cause we can not calculate it in the real numbers. Hope it makes it clear

[baudrunner]

The beauty of complex numbers is, in the first place, that they use the imaginary numbers, i.e., numbers that somebody, somehow, had to invent when he ran out of resources to try to explain certain solutions. The complex analysis we learn in high school, as much of the math, doesn´t have anything to do with the real use of these little invented fellows. Complex analysis can be used to solve equations that wouldn´t have an answer in the real plane and, for our special interest in TOE, it is significantly usefull that the complex sphere with the union of the infinite forms a space where solutions can be solved algebraically easier. Then we can use projections to return to the original space. This allow us to work with several dimensions and, even though we can not visualize them, they make sense mathematically. So, let´s think that math uses a lot of imagination. In the other hand, if the results of an operation yield to different results, we are facing a fallacy. I would like to take a look to that fake operation you guys are trying to solve.

Well, okay, hanzoganz, since you asked for it I will provide it for you. The use of the j operator in solving electronic circuit problems can be explained quite elegantly. Incidentally, j is used because the conventional symbol of i is used in electronic engineering to denote electric current, measured in amperes.

In the absence of a functioning LaTeX implementation on this board I have created a two page Adobe Acrobat compatible .pdf file with minimal mathematics but coherent explanations for your study. It can be read by clicking on this link.

[hanzoganz]

That is a very nice application of complex numbers, thou not of complex analysis. It is like using real numbers or using real analyis, two things that are completely different. Anyways, I like the example. I used poles and ceros, i.e. complex roots of a quadratic equations or characteristic equation to find stability of a point of levitation in my bachelors thesis.
Complex analysis has to do more with analytical functions and mappings from one space to other.

cheers...

[baudrunner]

Originally Posted by hanzoganz That is a very nice application of complex numbers, thou not of complex analysis. It is like using real numbers or using real analyis, two things that are completely different. Anyways, I like the example. I used poles and ceros, i.e. complex roots of a quadratic equations or characteristic equation to find stability of a point of levitation in my bachelors thesis. Complex analysis has to do more with analytical functions and mappings from one space to other.cheers...

That was the point. To explain the practical application of imaginary numbers in the real world to solve real world problems. There is no point in using the imaginary number i if there is no reduction of it to a real number in your calculations, regardless of whether you are dealing with complex numbers or doing a "complex analysis", and that is what I was explaining.

The presentation came across as understandable and simple because it is always my intent to project understanding however complicated the concept, because I understand it, therefore you will too. There is much to be said for clarity. The biggest problem with education today is that the instructor is just as often as not a re-iterator, and incapable of projecting a complete understanding of the subject matter because they have a lack of it themselves, and projection is half the process of educating. Well, you know what they say - those that can, do, those that can't, teach.

I would like to review your example of a complex analysis using imaginary numbers, hanzoganz, as long as it is not too far off the wall.

[hanzoganz]

I agree with you when talking about education. I was a high school teacher myself and came to see that a lot of teacher don`t know and don´t care about the real knowledge.

I also agree that once one knows something, he can share it. That`s why I like this forum, `cause it gives me the oportunity to translate the lenguage of math to the ordinary lenguage.

Yes, you are right about the translation to real numbers but not quite, cause sometimes we don`t use the complex numbers to give results of calculationg but just to see where that point is. A negative number as a solution for a differential equation is good in the sense that, if you have a solution as y=exp{-4i} it is going to go to stability soon.

I recomend you read about Riemann Surfaces, it is not really complicated but it is gratifying for the mind, ´cause it deals with surfaces in many dimensions.

And other point about teaching. Yes, some that can´t do, teach; but the ones that are suppose to be able to do, after a while are supposed to teach aswell.

[baudrunner]

And other point about teaching. Yes, some that can´t do, teach; but the ones that are suppose to be able to do, after a while are supposed to teach aswell.

In the imaginary world.

Okay, I had some good teachers at the college level, in fact some were downright inspirational and largely responsible for stimulating my interest in the physical sciences. But I sure wish I had them when I needed them.

I'll see if I can find Riemann surfaces interesting but my intuition tells me that it's just more math without purpose, and I really, really hate that.

[Mohan.C]

I don't know much on how to teach.

But I have to more results like i cannot be infinite and i cannot be negative it ie. -1< i <infinity.
I am giving my fake math as hanzoganz said because i dont think people are really interested in this.
Guille, I would like to as you you have come across this complex solution you were talking about which could prevent such absurd values.