Infinite Resistance

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Re: Infinite Resistance

Originally posted by physis: Charlie, I'm concerned, you're lacking you're typical tone of conviction.
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A great man once wrote,
No degree of belief, not even the deepest of convictions, can bring about truth.
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(Actually, that was me. It?s not bad. I think I?ll copyright it. )

Mathematics itself hold its own truths. It needs no emphatic words of mine to sustain its truths.
 
Re: Infinite Resistance

Charlie, doesn't lim log(x) as x goes to zero approach negative infinity? I have been told that negative and positive infinities are the same point. Does this start another wild discussion?
 
Re: Infinite Resistance

I did say that it "decreases without bound." That was intended to mean that it is negative, and keeps getting more negative.

I have not encountered the notion that positive and negative infinities are the same.
 
Re: Infinite Resistance

Speaking of that, lets go back in time about 13.8 billion years or so to the big bang. That is not negative infinity but why wouldn't it be? Can you go further back in time? Can you go back to say, 15 billion years? Did time exist then? What was there at that time? :D
 
Re: Infinite Resistance

physis wrote:
Rob, I talked to the guy about the spelling and he said you should be more concerned with the post before that one.
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o.k.
but please clarify the "post before that one". I'm not sure if two people are speaking there, or just one.
Is that post something from a math publication, with your comments interspersed? Or something you composed entirely? Or another person debating with him/herself?

it seems like some solid assertions, mixed with some interpretations & unanswered questions.

if you can clarify a bit, maybe I'll be able to take a shot at it.

(but be forewarned...the complex domain is a whole different game. As such, I could argue right now that you've changed the rules and all bets are off.)

:)
 
Re: Infinite Resistance

That's two people Rob. The mathmatical assertions belong to somebody else. The additional commentary is my limited understanding of what it describes. I wasn't writing a thesis I was trying to include enough information that someone could challenge the math. :)
 
Re: Infinite Resistance

That's two people Rob. The mathmatical assertions belong to somebody else. The additional commentary is my limited understanding of what it describes. I wasn't writing a thesis I was trying to include enough information that someone could challenge the math.
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physis: o.k., then please break it up into (ref. source) and (your interpretation). When all mixed together, I'm not sure what needs proving. If, for instance, you state what a symbol represents, but it really meant something else in the reference, we'll be chasing our tails.
also, please list the outside source. it helps to know the context of the statement, and the credibility of those making it. (i.e. I don't want to try to decode the visions of Miss Cleo)

:D

(but be forewarned...the complex domain is a whole different game.
Different enough to allow X/0?
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why certainly (maybe). it's different enough to define the square root of a negative number, when everyone knows that you can't square a real number and create a negative number.

(by the way, is the complex domain pure fantasy? of course not. but it's A.C. analysis now, not just the real subset expressed by Ohm's Law V=IR. that is to say, real numbers are covered by complex numbers, but complex numbers are not covered by real numbers. So be careful. all streets don't run both ways, and some are dead-ends.)


:eek:
 
Re: Infinite Resistance

This is what I said directly befor listing the variables.

These are my best guesses at the variables. They're not defined and my deductions may be wrong.
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I hope this helps.

You really don't expect me to beleive that you are somehow being missled do you.

Edit: There's nothing paticularly obscure about complex infinity. You have as much access to that math as anyone else. If I gave you more information I'm sure you would ask me to defend that as well. :)

[ December 13, 2004, 07:10 PM: Message edited by: physis ]
 
Re: Infinite Resistance

This is the math (I don't care who want it to be associated with)

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=∞.
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This is where I altered it. I paraphrased it from I think C* to "complex infinity".

Infinity in this case is complex infinity.
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Is it clearer now?

Edit: :)

[ December 13, 2004, 07:43 PM: Message edited by: physis ]
 
Re: Infinite Resistance

Hello Peter, I agree.

Originally posted by peter d:
If a resistor snaps in the woods, and no one is there to hear it, does it make a sound?
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We don't care!!!!!!!! :D

In short this thread is a NON (as in ZERO, ZILCH, NOTA, NOTHING, etc...) issue multiplied by more ZERO, ZILCH, NOTA, NOTHING, etc... (Can we imagine one of those mirror boxes that were in the bars of the 80's)

Thank you very much. :D :D :D

Roger

[ December 13, 2004, 08:37 PM: Message edited by: roger ]
 
Re: Infinite Resistance

Originally posted by physis: Is it clearer now?
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It?s perfectly clear now. That is because I found the web site that you have been using for your attempts to declare that division by zero can have meaning. As I suspected, you have taken it out of context. But I see the source of the confusion, and admit how easy it would be to miss the single most important detail contained within that web site?s descriptions.

In electrical engineering, we often must deal with ?complex numbers.? That set of numbers includes the ?real numbers? and numbers that involve taking the square root of negative one. We can plot information on a standard X ? Y graph in which the horizontal axis represents the real numbers (e.g., real power, or KW), and the vertical axis represents the complex numbers (e.g., reactive power, or KVAR). This type of X ? Y graph is said to have been laid out within the ?complex plane.? That phrase means that a flat sheet of paper (representing a plane) is used to model both real numbers and complex numbers. All of electrical analysis, including a formal analysis of the original question about Ohm?s Law for an open circuit, can be carried out within the limitations of the ?complex plane.? The rules for this ?complex plane? include the rule that division by zero is ?undefined.?

What you are describing, what you found on the Internet, is not the ?complex plane.? Rather, it is the ?extended complex plane.? It was envisioned by a highly talented theoretical mathematician almost 400 years ago. The ?extended? part of his vision was allowing the plane to include the point at which two parallel lines intersect. That point, the so-called ?point at infinity,? does not literally exist (but for that matter, neither does the square root of negative one). But if you permit the theoretical ?pint at infinity? (side note: that was an accidental typo, but I think I?ll leave it there :D ) to exist, then you can conclude that ?complex infinity? is a number that can be reached by dividing 1 by zero. You can next establish a definition for ?1 / 0,? as you have pointed out. You cannot, however, take the next step of multiplying both sides of that definition by zero, and conclude that zero times ?complex infinity? equals one. The web site does state that clearly.

So I will be willing to grant your statement that "1 / 0" has a definition, and that that definition gives it a value of ?complex infinity,? if you will grant my assertions that (1) That definition only applies within the ?extended complex plane,? and (2) The ?extended complex plane? cannot be used in any electrical or electrical engineering context.
 
Re: Infinite Resistance

physis wrote:
This is where I altered it. I paraphrased it from I think C* to "complex infinity".
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yes, I know. that's why I asked. You weren't satified with just paraphrasing infinity=zero, were you? :p

charlie b wrote:
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.
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see, charlieb asked the same question. (missed your response on the last past thru, charlieb)(by the way, are new posts appearing inserted mid-thread out of nowhere, or have I been staring at infinity too long?)
:roll: )
 
Re: Infinite Resistance

rob321,
Who let this guy in?
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You did. I was simply interested in your babble, and I actually think my post is as on the money as any of yours. :D

Face it, (and this will knock your socks off) you are talking about nothing, no matter how much intelligence you are trying to show.

Roger

[ December 13, 2004, 09:52 PM: Message edited by: roger ]
 
Re: Infinite Resistance

Face it, (and this will knock your socks off) you are talking about nothing, no matter how much intelligence you are trying to show.
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no...actually we're talking about what happens to physical systems as you approach limit conditions. Many examples were given already by many posters, such as short circuits, lightning discharges, & open circuits. In fact, every time a switch closes, we can look at how we get from infinity to zero. (if we want to).

but whether or not such talk is as useful as the wet-finger/live-circuit test is a matter of opinion, I guess.

WHOA! where'd my socks go?

lolololol
 
Re: Infinite Resistance

I think infinity is so large that it covers the entire complex plane like a carpet.
 
Re: Infinite Resistance

Rattus, If you want a really really good distortion guitar amp you're gonna have to!

:cool:

Edit : I think i'm responding to you're signature.

[ December 13, 2004, 11:04 PM: Message edited by: physis ]
 
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