Infinite Resistance
- Thread starter physis
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physis
Senior Member
Re: Infinite Resistance
I can see that most of my trouble is with the calculus types.
Ok,
I've got one source claiming that devide by zero is undefined. (Just so you don't think we're all running around dividing everything we can find by zero). But in some contexts it can be considered as defined. The following is one of those contexts. I don't know how valid the assertion is but I'm sure some of you guys and Charlie B. will have your BS scanners running. And if I don't describe it correctly it's because I can't find much clear info on the web and I'm a little fuzzy on some of it.
z/0 for zЄC*≠0 in the "extended complex plane" (C*) is defined as the quantity "complex infinity". This definition expresses the fact that for z≠0, lim(ω→0)z/ω=∞. Infinity in this case is complex infinity.
From this it's asserted that 1/0=∞ is a formal statement permitted in complex infinity.
These are my best guesses at the variables. They're not defined and my deductions may be wrong.
C* = complex infinity. It is the complex plane (I'll describe) with a "point at infinity" attached. (I'm still not getting that).
Є = infitesimal quantity or point ( I can't tell which) contained in the extended complex plane.
ω = I think this is just a variable.
z = I think this is just a variable or it may be the Gaussian intigers. Z = {a + bi :a,bЄZ} the ring of intigers of K = Q(i)). (The "z" used wasn't the symbol for that though).
The "complex plane" is defined by the real vector axis 1 and the imaginary vector axis i, the value of i is √-1. The complex numbers contained on the complex plane are the coordinants of the real axis and the imaginary axis. The complex plane together with the point at infinity (that I still don't get ( I know what a point at infinity is, I dont know how it interfaces with the plane)) is denoted by C U {∞} and is the "extended complex plane" or "complex infinity" or C*. This is also known as the Riemann sphere.
Is there a concensus on 1/∞=0?
See, you guy's aren't the only people I don't listen to. I don't listen to that guest poster either. She's a calculus type too. Wasn't very happy with my messin with zeros and infinities.
Steve, never mind about quantum mechanics. I think that's what you use to cure the most stubern cases of mathenjoymentitis. Somehow it lacks elegance.
I can see that most of my trouble is with the calculus types.
Ok, I've got one source claiming that devide by zero is undefined. (Just so you don't think we're all running around dividing everything we can find by zero). But in some contexts it can be considered as defined. The following is one of those contexts. I don't know how valid the assertion is but I'm sure some of you guys and Charlie B. will have your BS scanners running. And if I don't describe it correctly it's because I can't find much clear info on the web and I'm a little fuzzy on some of it.
z/0 for zЄC*≠0 in the "extended complex plane" (C*) is defined as the quantity "complex infinity". This definition expresses the fact that for z≠0, lim(ω→0)z/ω=∞. Infinity in this case is complex infinity.
From this it's asserted that 1/0=∞ is a formal statement permitted in complex infinity.
These are my best guesses at the variables. They're not defined and my deductions may be wrong.
C* = complex infinity. It is the complex plane (I'll describe) with a "point at infinity" attached. (I'm still not getting that).
Є = infitesimal quantity or point ( I can't tell which) contained in the extended complex plane.
ω = I think this is just a variable.
z = I think this is just a variable or it may be the Gaussian intigers. Z = {a + bi :a,bЄZ} the ring of intigers of K = Q(i)). (The "z" used wasn't the symbol for that though).
The "complex plane" is defined by the real vector axis 1 and the imaginary vector axis i, the value of i is √-1. The complex numbers contained on the complex plane are the coordinants of the real axis and the imaginary axis. The complex plane together with the point at infinity (that I still don't get ( I know what a point at infinity is, I dont know how it interfaces with the plane)) is denoted by C U {∞} and is the "extended complex plane" or "complex infinity" or C*. This is also known as the Riemann sphere.
Is there a concensus on 1/∞=0?
See, you guy's aren't the only people I don't listen to. I don't listen to that guest poster either. She's a calculus type too. Wasn't very happy with my messin with zeros and infinities.
Steve, never mind about quantum mechanics. I think that's what you use to cure the most stubern cases of mathenjoymentitis.
Somehow it lacks elegance.
physis
Senior Member
Re: Infinite Resistance
original entity. The numbers it contains, by themselves, have no useful meaning. They only have meaning relative to other numbers. Thinking of zero and infinity or any other value as discrete entities necessarily removes at least
some of their meaning. The way I think of it, zero and infinity are as much a connected duality as electricity and magnetism.
The problem with division by zero is that it's terribbly disruptive. It's not allowed as a matter of convention because it introduces chaos. From a practicle stand point it makes perfect sense to disallow it. As long as you do
we can go about our math business immune to it's destrucive effects. The choise to not divide by zero is not one made by math, it's made the users of math. Math doesn't care that it has an integral anomaly, you do. Using convention is important if you want order. But it doesn't redifine the phenomenon. You're so used to the way you use it that you've replaced it with what you use.
There are two things the divide by zero math tricks have in common. Dividing by zero is one. The other is dividing zero. If there's something that can't be done it's divide zero. But that's allowed because it's not destructive to the equation, unless zero is the divisor.
Phweew
0→∞ is a single entity. It contains all of the positive elements in the universe. You're free to yank the zero off of it and play with it seperately if you like. But what you do with the zero seperately isn't necessarily related to the
original entity. The numbers it contains, by themselves, have no useful meaning. They only have meaning relative to other numbers. Thinking of zero and infinity or any other value as discrete entities necessarily removes at least
some of their meaning. The way I think of it, zero and infinity are as much a connected duality as electricity and magnetism.
The problem with division by zero is that it's terribbly disruptive. It's not allowed as a matter of convention because it introduces chaos. From a practicle stand point it makes perfect sense to disallow it. As long as you do
we can go about our math business immune to it's destrucive effects. The choise to not divide by zero is not one made by math, it's made the users of math. Math doesn't care that it has an integral anomaly, you do. Using convention is important if you want order. But it doesn't redifine the phenomenon. You're so used to the way you use it that you've replaced it with what you use.
There are two things the divide by zero math tricks have in common. Dividing by zero is one. The other is dividing zero. If there's something that can't be done it's divide zero. But that's allowed because it's not destructive to the equation, unless zero is the divisor.
Phweew
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Re: Infinite Resistance
Tricky...
Man, I don't understand math guys...
Hmm.Originally posted by steve66:
I agree
Tricky...
Man, I don't understand math guys...
charlie
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Re: Infinite Resistance
I don't know which is worse, the guys that really understand this stuff or those of us that have kept up with the thread but don't understand what they are saying (I am in the latter group).
I don't know which is worse, the guys that really understand this stuff or those of us that have kept up with the thread but don't understand what they are saying (I am in the latter group).
physis
Senior Member
Re: Infinite Resistance
If two old guys are playing a game of checkers in the park, no one has an uncontainable urge to run over to them and yell "I can't take it anymore, you two guys are boring me to death".
Rob, I talked to the guy about the spelling and he said you should be more concerned with the post before that one.
Edit: 80 posts and all of a sudden nobody cares. It's because I've come up with the goods.
[ December 12, 2004, 01:45 PM: Message edited by: physis ]
If two old guys are playing a game of checkers in the park, no one has an uncontainable urge to run over to them and yell "I can't take it anymore, you two guys are boring me to death".
Rob, I talked to the guy about the spelling and he said you should be more concerned with the post before that one.
Edit: 80 posts and all of a sudden nobody cares. It's because I've come up with the goods.
[ December 12, 2004, 01:45 PM: Message edited by: physis ]
Re: Infinite Resistance
Physis
If it where not for threads like this one where a lot of it is in fun I wouldn't even visit this site.
But an old timer like myself that didn't take a lot of interest in math doesn't know half the time if the answers are serious or BS.
Physis
If it where not for threads like this one where a lot of it is in fun I wouldn't even visit this site.
But an old timer like myself that didn't take a lot of interest in math doesn't know half the time if the answers are serious or BS.
physis
Senior Member
Re: Infinite Resistance
Ronaldrc, if it's not fuzzy it's not fun. What would be the point in debating 2 X 5.
What's interesting to me is that this thread has a lot of the same attributes as a polital arguement.
Edit: corrected a miss spelling for Rob
[ December 12, 2004, 03:07 PM: Message edited by: physis ]
Ronaldrc, if it's not fuzzy it's not fun. What would be the point in debating 2 X 5.
What's interesting to me is that this thread has a lot of the same attributes as a polital arguement.
Edit: corrected a miss spelling for Rob
[ December 12, 2004, 03:07 PM: Message edited by: physis ]
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Re: Infinite Resistance
You statement is also true. So was mine: 42sin(x)/x approaches 42, as x approaches 0
Yes. I never said it didn?t.
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Re: Infinite Resistance
The English translation of that phrase is that ?z/0 , where ?z? is an element of the complex plane, but z does not have the value of zero. . . .? That funny looking ?E? means ?is an element of the set.? I suspect that you have taken a definition out of context. I don?t think there is a math book that formally defines division by zero.
This may be where you are taking the information out of context. This is a legitimate mathematical statement. The concept of infinity can be defined in terms of limits. But to state that something increases without bound is not the same thing as saying that infinity itself is a number, nor that you could reach that number by dividing 1 by 0.
Nope. Not giving you that one.
Not!
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Re: Infinite Resistance
1 / 0 = "Cannot divide by zero"
I tried that with the calculator supplied with "Windows" (Programs > Accessories > Calculator)
1 / 0 = "Cannot divide by zero"
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Re: Infinite Resistance
The number "0" does not appear on a slide rule, and the log of 0 is undefined (i.e., decreases without bound as you approach zero), as you (my fellow EE) bloody well know!
[ December 13, 2004, 10:15 AM: Message edited by: charlie b ]
The number "0" does not appear on a slide rule, and the log of 0 is undefined (i.e., decreases without bound as you approach zero), as you (my fellow EE) bloody well know!
[ December 13, 2004, 10:15 AM: Message edited by: charlie b ]
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