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Old 02-25-2002, 10:45 PM   #26
Boo
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How about any # divided by zero?

You can't? Like what do you mean you can't? 5/0 = undefined

Try it on a caluclator or on the PC.

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Old 02-25-2002, 10:56 PM   #27
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Quote:
Originally posted by *labRat*

hardly - it's also better known as i in the mathie circles and j in engineering circles (specifically electrical). it's extensively used in electromagnetics and controls to accurately model systems. without them there wouldn't be a hell of a lot of technology as we know it today.

i personally prefer my complex numbers in polar form.

--craig
HAHAHA... whatever

Show me a real system where i/j actually manifests itself and I'll give you a Nobel Prize...

just because you can use it in solving equations doesnt mean it is physically realizable..

infact, that is the entire premise behind most power engineering (mr knowitall)...

that is...

Power Output = Real (Complex Power Output)

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Old 02-25-2002, 10:57 PM   #28
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have you ever tried painting the outside of Gabriel's Horn? you can't, it's impossible. but you sure can fill it with paint.

crazy?

note: Gabriel's Horn is a cone like object found by taking y=1/x [1,inf) and rotating it around the x-axis.

--craig

Last edited by labRat; 02-25-2002 at 11:00 PM.
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Old 02-25-2002, 11:02 PM   #29
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[
Quote:
(i = squareroot of -1 a number which exists only in theory in case you dont know)
just to clarify, i is defined (in the complex sense) as i squared=-1,
since the square root has both positive and negative roots.
i.e. if i=-(sqrt -1), than i=-i, which to my knowledge cannot be true. i think.
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Old 02-25-2002, 11:10 PM   #30
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true dat ^^^

in any case, it doesnt exist, any value which includes it can by definition not be realizable in any physical system..

which i guess.. means then that it exists in the non-physical universe only..

but so does the club where Tenaglia never leaves..

and so does my 12 inch sausage



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Old 02-25-2002, 11:18 PM   #31
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Quote:
Originally posted by ADT
Show me a real system where i/j actually manifests itself and I'll give you a Nobel Prize...
uh, well. since i/j are considered imaginary i don't think you'll be finding them in any real systems.

Quote:
infact, that is the entire premise behind most power engineering (mr knowitall)...
i don't actually knowitall, but i think i know a fair bit. i also know that power engineering falls in the realm of electromagnetics.

Quote:
Power Output = Real (Complex Power Output)
thanks. i did not know that. that's just the same as saying 1=1. but what about reactive and complex power - both those involve the imaginary portions of the total power. and you can't dismiss the importance of these relations. you can't solve any electrical network involving capacitance and inductance without the use of imaginary numbers.

all numbers are just a representation of something. can you actually show me what the number 3 is? other than showing me three objects?

i'm tired and going to bed now.

toodles.

--craig
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Old 02-25-2002, 11:18 PM   #32
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.9999... is 1
they are one and the same.

if they are different then there must be some interval a | .999... < a < 1 .

as the number of nines goes to infinity, a goes to zero, hence the difference between the two numbers dissapears, and they are the same.
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Old 02-25-2002, 11:24 PM   #33
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Old 02-25-2002, 11:30 PM   #34
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according to my abacus...it's 3
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Old 02-25-2002, 11:35 PM   #35
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deep: i got's my kettle here, but where's my pot? they're both black in case you didn't know.

one more before i go - i can't remember it completely, maybe it'll come to me in the morn'. it was from the best calculus prof ever, Stanley Lipshitz. This was from his first lecture and it was regarding proof.

He drew a sheep on the board and proclaimed it to be a sheep. Then he drew a three legged sheep, and he still said that it was a sheep even though it only had three legs. Then he asked us if a three-legged animal was a sheep. Of course the answer is no, but you couldn't be for certain. So you had to prove that it was/wasn't a sheep.

Something like that.

genious, pure genious.

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Old 02-25-2002, 11:39 PM   #36
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Quote:
Originally posted by *labRat*
deep: i got's my kettle here, but where's my pot? they're both black in case you didn't know.
oh brother, mama knows, mama knows. it's teh ironay you know

ps. it's 'genius'

pps. I know, it's late

ppps. that doesn't free you from the obligations to detail that is being nerd

pppps. nerd
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Old 02-25-2002, 11:49 PM   #37
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this is really cute.
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Old 02-25-2002, 11:59 PM   #38
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Quote:
Originally posted by *labRat*

but what about reactive and complex power - both those involve the imaginary portions of the total power. and you can't dismiss the importance of these relations. you can't solve any electrical network involving capacitance and inductance without the use of imaginary numbers.
imaginary numbers are just a trick to make the equations easier to deal with, they are in no way essential to the solution or do they represent anything that is actually occuring in the system..

reactive and complex power are the types of power I was referring to, and they do not represent any actual power drain..

infact, eliminating the complex part of the power gives you the actual power drain..

the complex power elements exist only to represent the transient nature of the system in a mathematical form

example:

picture a phasor rotating in the complex plane..

if that vector represents a wave, the actual wave is the real projection of the vector... so what is the imaginary projection? unless theres some transverse universe where that projection is manifesting itself.. nothing!

i is not a real number (no pun intended ), its a mathematical trick..

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Old 02-26-2002, 07:57 AM   #39
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Quote:
Originally posted by ADT


imaginary numbers are just a trick to make the equations easier to deal with, they are in no way essential to the solution or do they represent anything that is actually occuring in the system..
umber (no pun intended ), its a mathematical trick..


Without i conservation of energy and momentum would not hold for electrons......without i you could not solve the problem of electron tunneling. There would be no transistors and hence no computers.

......there are many mathematical problems which need i to be solved. Granted, most of these involve black holes..... but there are a few that are relavent on earth.



dan.
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Old 02-26-2002, 08:18 AM   #40
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Quote:
Originally posted by ADT
Show me a real system where i/j actually manifests itself and I'll give you a Nobel Prize...
YAY.

Impedance is a very 'real' thing (if that's the real you mean), and it is entirely based on i/j.

As someone mentioned, j is no more or less existential than 1.

-jM
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Old 02-26-2002, 08:33 AM   #41
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And in plenty of calculations of impedances you end up with terms in the denominators of the form

(-(cos^2x + sin^2x) ) ^(1/2)

Now of course you can argue that there is no 'need' to use complex notation to solve this, but they are semantically equivalent, and thus doing it using trig or imaginary numbers must also be semantically equivalent: ie. both are just as existential.

You can draw one of two conclusions from that.

1. That complex numbers exist as much as real ones do
2. That real numbers are as imaginary as complex ones

I think both are true.

YAY.

ANd though, yes, it is the projection of the phasor that gives the real portion, but for most applications, knowing merely the 'real' portion is not enough to solve the problem. I am using impedance as an example because it is familiar (the 'resistance' of any speaker or motor is almost always zero) but there are countless others.

THe projection of the phasor on the imaginary axis plays a big part in the loss of 'real' energy in power systems. (The dot product of these vectors is used commonly which yields a scalar, ie. energy)

-jM
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Old 02-26-2002, 08:42 AM   #42
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It's all coming back to me now....

Math sucks, or rather, I really suck at math.

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Old 02-26-2002, 08:44 AM   #43
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Quote:
Originally posted by deep
ps. it's 'genius'
hey - i didn't say i was an english major. if it were up to me i'd spell it genjus ... i'm sure that ADT would spell it genus (since i is not real)

and by the way, it's j not i. get it right people. i is for weenies.

and 'imaginary' numbers are very much as legit as real numbers. don't take the nominclature so literally.

Quote:
the complex power elements exist only to represent the transient nature of the system in a mathematical form
exactly, so without imaginary numbers you wouldn't be able to solve any such equations involving transients. how would you be able to find out what the phase of an AC system is, or whether the voltage is a leading or laging the current? how would you accurately model a power system without complex equations - please tell me because i'm dying to know.

Quote:
(imaginary numbers) are in no way essential to the solution or do they represent anything that is actually occuring in the system
as a additional assignment can you please solve the following for me : z^2 = -1 without the use of imaginary numbers.

[hippie]think outside the box man[/hippie]

--craig
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Old 02-26-2002, 09:07 AM   #44
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Quote:
Originally posted by Bass-Invader
.9999... is 1
they are one and the same.

if they are different then there must be some interval a | .999... < a < 1 .

as the number of nines goes to infinity, a goes to zero, hence the difference between the two numbers dissapears, and they are the same.
i wouldn't tell people that .9999.... is the same as 1 since this is not the case. performing roundoffs can be potentially very dangerous.


about complex numbers, i think debating whether they are "tangible" or not is stupid. the bottom line is that they help you. there are many things you can't represent without them, and thus, they are very useful.
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Old 02-26-2002, 11:50 AM   #45
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Quote:
Originally posted by miguel


i wouldn't tell people that .9999.... is the same as 1 since this is not the case. performing roundoffs can be potentially very dangerous.

I'm not rounding. They are the same.
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Old 02-26-2002, 12:05 PM   #46
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Quote:
Originally posted by miguel


i wouldn't tell people that .9999.... is the same as 1 since this is not the case. performing roundoffs can be potentially very dangerous.

It is not rounding off, it is the result of an infinite sum.

.99999.... = .9 + .09 + .009 + .0009 + ....
= .9 + .9/10 + .9/100 + .9/1000 + ....
= .9 + .9(1/10)^1 + .9(1/10)^2 + ..9(1/10)^3 + ....
= .9/(1-.1)
= 1

http://www.cut-the-knot.com/pythagoras/a_series.html



dan.
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Old 02-26-2002, 12:12 PM   #47
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Quote:
Originally posted by miguel
performing roundoffs can be potentially very dangerous.
Not for a gymnast.

Cheers ... Ian
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Old 02-26-2002, 12:34 PM   #48
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Old 02-26-2002, 12:41 PM   #49
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jesus, are we still talking about the .9999.... thing? How about we talk about the golden mean or something instead?

basically, you take the Fibonacci series:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 , etc (take the last two numbers, add them together to get the next number)

then take the ratio of any 2 numbers in the series:

1/1 = 1
2/1/ = 2
3/2 = 1.5
5/3 = 1.6666
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538
34/21 = 1.61904...

etc, etc.. and this number approaches the number 'phi' (not pi), which is 1.6180339887499, etc, etc to infinity.

If you have a rectangle whose sides are related by phi (say, for instance, 13 x 8), that rectangle is said to be a Golden Rectangle. It has the interesting property that, if you create a new rectangle by 'swinging' the long side around one of its ends to create a new long side, then that new rectangle is also Golden.





Now, for some reason, this is ratio is replicated in nature everywhere, in shells, in plant life, etc.

(also, artists have used it forever because the eye finds things with this ratio 'pleasing' )
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Old 02-26-2002, 01:50 PM   #50
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Quote:
Originally posted by Sporty Dan



It is not rounding off, it is the result of an infinite sum.

.99999.... = .9 + .09 + .009 + .0009 + ....
= .9 + .9/10 + .9/100 + .9/1000 + ....
= .9 + .9(1/10)^1 + .9(1/10)^2 + ..9(1/10)^3 + ....
= .9/(1-.1)
= 1

http://www.cut-the-knot.com/pythagoras/a_series.html



dan.
hah ! silly me

(and i'm a math major too)
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