Is 5 + 3i an imaginary number?
I don't think so.
What does i represent? Simply an unknown number?
Technically, it is a complex number, consisting of a real part (the 5) and the imaginary part (the 3i). On the other hand, an imaginary number can simply be thought of as a complex number where the real part is zero, and vice versa.
I always hated algebra.
I didn't mind Algebra or Trigonometry... but I hated Geometry.
.I disagree!1!!!111bunchof1's!!1!11 L0l-cakez! Rofl-copter! 1 c4n h4z ch33zburg3r!
Sounds like how capitalists scientifically prove that it is the best system.
More like how communists scientifically prove that their system is the best.
Of course, when that fails to pass the BS meter, the commies haul out their guns and point them at their intended victims. That's when it gets interesting...
More like how communists scientifically prove that their system is the best.
Of course, when that fails to pass the BS meter, the commies haul out their guns and point them at their intended victims. That's when it gets interesting...
Unless they are Chinese or something.
And the recent crisis showed a lot of BS as well.
On math: I never minded it much. It became difficult only after I got to a technology university.
Of course my math skills have deteriorated with time.
Um... any real-world application of algebra isn't finding numbers for the sake of finding numbers. It's finding a number because it's useful.
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lol wut?
[...] as it shows that what I said cannot be refuted.
Not really.
It doesn't prove anything. That's kinda the reason it's bad debate tactics.
I think it's because Goldy had some smart-@$$ comment on what I said about communists, something that ORC_Nashira saw as a personal attack and deleted.
I don't worry too much about ad hominem attacks, as it shows that what I said cannot be refuted.
Please. It is only because you didn't like my rebuttle. You linked weapons and communist and I linked weapons and right-wingers who shoot politicians. But right-wingers do not like the truth so they just censore stuff because they cannot debate and face truth. I am glad that big brother ORC helped you. Pretty ironic since you believe that higher authorities can only abuse their power. I guest it only aplays to stuff you do not like.
Wow. And no, I'm not referring to the life destroying game.
Internet be damned.
In goldomark's defense; everything can be refuted.
In ORC_nashira's defense; doing the job.
In iquinn's defense; opinions will always be met with adversity. Especially if they are expressed.
Can't we all just agree to disagree?
We're all pretty here.
Is 5 + 3i an imaginary number?
its not a number. '+' is not a valid mathematical sign.
does 0.9999... equal 1
That one's fun. I'm still of the opening they're the same, but it's always fun to see counter-arguments.
does 0.9999... equal 1
That one's fun. I'm still of the opening they're the same, but it's always fun to see counter-arguments.
It's not 1 in the stricktest sense, but it could be treated as 1 for practical reasons
X = 0.99999999999999...
-> multiply by 10
10X = 9.9999999999...
-> minus X
9X = 9
-> divide by 9
X = 1
So it's actually exactly the same. But you can still argue it's not the same, based on which rules for calculating with Infinites you follow... not everyone agrees on those.
EDIT: Your post may be safe, Plu. I quoted and you did not. We'll see what happens.
EDITAGAIN: Oh, and I do agree with you. I was just irritated by someone using a personal interpretation of a recent event as some sort of definitive proof.
EDITSOMEMORE: Wikileaks task force? The post I quoted is still there but mine is gone. That's just ... wikileaks task force. Damn.
While not an accepted mathematical symbol, it is espressive of a deviation, in statistics and as they are used by machinsts, tool-makers, and engineers.
The question should really be "are 5 + 3i or 5 - 3i an imaginary numbers?"
The ± sign just means plus (+) or minus (-). There are actually two equations being presented.
The question should really be "are 5 + 3i or 5 - 3i an imaginary numbers?"
Qube was being a "smartaleck" as Piggles used the underline command for an addition symbol instead of "±" .
Error: False presumption, Piggles used the proper symbol. Qube just doesn't acknowledge of the symbol as proper in mathematics.
Sensory data corrupted: I need to hibernate soon...
It could be read as "is 5, give or take 3i, an imaginary number?"
It still doesn't sound right though.
Proper question should probaby be "is a belonging to A where A={x: x
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≥5-3i and x
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≤5+3i} an imaginary number?"
(sorry for lack of actual symbols, didn't know how to put them in"
You can actually prove it's 1. Check this:
X = 0.99999999999999...
-> multiply by 10
10X = 9.9999999999...
-> minus X
9X = 9
-> divide by 9
X = 1
Sorry Plu, but there's a capital mistake in this proof (I bolded it): You may not substract unknown variables.It's just like 'divide by X'. Unless you first can prove that you may divide by X (a.k.a. that X can't be zero), you can't divide by X.
Same here: We're trying to calculate the value of 0.9999... (or X). But suppose the numerical value of 0.9999 actually equals infinity (instead of 1) ...
You just did '10X-X', which comes down to infinity minus infinity, which can't be done.
X = inf
10X = inf
10X-X = inf-inf
9X = 9
X = 1. which is wrong, as X was inf
That doesn't look very unknown to me.
The proof is also given on the Wiki page along with a series of other proofs :P
en.wikipedia.org/wiki/0.999...
Anyway my formal math training isn't done yet for the time being, so I'll probably learn a few things as I proceed.
How is X an unknown variable? It's 0.999999...
but the point is that we don't know what 0.999999... is, ins't it? (because you're proving its actually 1)
You're assuming its a real number, so you assume you can use real operations
- you can multiply any real number with an other real number (if you have X, you can do 10*X)
- you can add any real number with an other real number
- you can substract any real number with an other real number
- you can only divide by a real number, if that number is not zero
However, unless you first prove (or assume) that 0.999999... real number, you can't do such operations.
And that is what the wikipedia page you linked says: "0.999... denotes a real number that can be shown to be the number one." So on the wikipage, they start with the base assumption that 0.999 is the (real) number 1.
By defining "0.999... denotes a real number that can be shown to be the number one", I can show a much shorter proof: "0.999... equals 1". By definition. Q.E.D.
However, To give an other example, if I define 0.999... as
Limit(X->positive infinity) for 1-1/(10 to the power X).
Then, mathematically, the only correct statement is that
0.999... approaches 1, as opposite to 0.999... equals 1.
(which, btw also uses the '=' sign; to confuse people ... )
But anyway, this is what I meant about being able to discuss it for so long... it's both exactly 1 and not exactly 1 at the same time.
Thing is though, that I'm not a "scientist"2, I'm an "engineer". Which, naturally, brings us back to the old joke about the difference between a mathematician and the mechanic4, which illustrates the difference between applied and theoretical.
________
1Let's see... I think it goes something like...
Women = time * money ("Women take time and money")
Since time = money ("time is money, friend!")
Women = money2
Since money = evil1/2 ("money is the root of all evil")
Women = (evil1/2)2
Women = evil
2Well, it says "computer science" on my diploma3, but any career I actually get will probably have "computer engineer" as the description, as opposed to "computer scientist".
3Or rather, it will once I get it. Registrar's office said they'll be mailed the 15th...
4A mathematician and a mechanic are both at a line, with a beautiful naked woman at the other end of the room. They are told that with each step they can halve the difference between them and the woman, but never more then that. They can take an unlimited number of steps. The mathematician exclaims "But we'll never get there!" to which the mechanic replies "but we can get close enough."
Disclaimer: I apologize for the sexist jokes in this post. I blame my math-major friend. She liked the sexist math jokes for some reason.
A mathematician and a mechanic are both at a line, with a beautiful naked woman at the other end of the room. They are told that with each step they can halve the difference between them and the woman, but never more then that. They can take an unlimited any number of steps. The mathematician exclaims "But we'll never get there!" to which the mechanic replies "but we can get close enough."
fixed
if the mathematician can take an unlimited amount of steps, he's in a collection of numbers superceiding the real numbers (being the real numbers and infinity, R U {+inf,-inf}. ( R being the collection of real numbers) )
While in R you need limits to work with infinity (and thus the mathematican will only be able to get near the woman), in R U {+inf,-inf}, you can work with infinity as a number. As such
- 2(+infinity) equals (+infinity)
- 1/(+infinity) equals zero
So, when taking an unlimited amount of steps, the distance between the woman and the mathematican will equal (1/2(+infinity)) which equals zero. So the mathematican would get there
Though the physisist will point out that the mathematican will die before getting there ...