Imaginary Numbers

Are complex numbers any more imaginary than real numbers? What makes pi more real than i?

Why was 1 afraid of 0.999...?
Because 0.999... is a doppelgänger that will kill him.

>>79
Saying it's an assumption means that there's a baser proof that's required.  There is no such requirement.  What I submitted was perfectly acceptable and it hardly matters who squawks about it.

You may as well just say "morons won't accept your conclusion".  Well, DUH, Mr Obvious!  Morons can't be persuaded by logic in the first place.  That's why they're morons!

It remains fully true and undeniable that 0.999... = 1.  It's easily demonstrated and that's all I care about.  That you seek to expend more breath on pointless points is amusing and sad.

(In case you weren't keeping track, I just PWNED THE FUCK out of you again.)

>>82
I have followed this debate.  Your detractor's points were valid, but split hairs as the whole of the matter is the undeniable truth of .999...=1.

>>82

You're an absolute idiot.

Any two real numbers that do not have at least one other number between them are equal.  Any number larger than 1 is also larger than .9999~repeating, and any number smaller than .9999~repeating is also smaller than 1.  So lets go for x such that x>.9999~repeating and x<1.  For X to be less than one, it has to have no nonzero digits to the left of the decimal point.  For X to be bigger than .9999~repeating, it has to follow the following condition:

Either the first decimal point we are considering has to be bigger than the number we are comparing it to, or equal to the number and repeat the test for the next digit over (this is easily deduced by changing this to the sum of 1/(10)^n terms).  For a number to be bigger than .9999~repeating, this implies that every single digit has to be 9, all the way to infinity... just like .9999~repeating is.

So there can't be another number between .9999~repeating and 1, so both numbers are equal.

>>82
Now I feel bad. As it turns out, I've done a disservice to mouth breathing inbred middle school dropouts everywhere.

"Saying it's an assumption means that there's a baser proof that's required.  There is no such requirement."

If it's acceptable to say "0.111... = 1/9" without proof, why not just simply state "0.999... = 1" without proof? Your "proof" that 0.999... = 1 depending on an assumption which you did not prove to be true.

>>85
M-M-M-M-MONSTER KILL
KILL
KILL
KILL

Is there a form of math that assigns pi as a single, whole value instead of 3.141... I don't mean the π symbol, but instead, π = 1?

>>88
Nope. 1 is reserved for the multiplicative identity. π is not the multiplicative identity. For one thing, π^2 does not equal π, but 1^2=1. π is also not within the integers because all integers are rational, whereas π is not. π will always be a number between two numbers a and b such that such that ak-k-k=k and bk-k-k-k=k. We usually call those two numbers "3" and "4." Again, although the base-10 decimal system is purely artificial, the integers, ordering, and rational numbers is essential. The essence of a number is in its properties and how it is assigned values that it associates with in certain ways like in those binary functions required for fields.

>>88
Ignore >>89 since he's made of fail.  Of course you could arbitrarily set π=1, by declaring that the ratio of a circle's circumference to its diameter is exactly 1.  That's how we ended up with the speed of light being EXACTLY 299,792,458 m/s ... the meter itself was redefined to match an exact value of the speed of light.

In other words, merely divide the entire number line by π, and you get what you want.  You just have to accept that the number line you have now is based upon a UNIT which you've defined to be π.

>>90
No, moron.  >>89 was right.  Pi still isn't an integer.  Sure you can arbitrarily redefine everything to fit a stupid idea, but if you set pi=1, you're not going to be happy with what 1 equals.  And the whole idea is made of fail.

>>90

Um, won't we have problems with π^2 ?

>>90
If you modify the numbers that way, addition would work the same, but multiplication would be quite different under the new system.

BITCHES DON'T KNOW 'BOUT MY MULTIPLICATIVE IDENTITY.

>>82
not undeniable.  it's denied all the fucking time, because it is a queer and a fag

>>91
You're the moron here.  If you simply define it to be 1, then it DOES become an integer.  As I said, just define the ratio of C to d as 1, and that becomes the basis for the number line.

We tolerate rotations being defined in units of 2π radians.  This can't be any different.

>>92
No, since π=1, then π²=1.

BTW, I am greatly enjoying this.

I honestly did.'t mean π = 1 specifically, And changing all other numbers to match π was a closer approximation of what I meant.  It just seems that since π is our universes angular geometric stabilizer, that there should be a kind of math that treats π as a single whole number.  If π was expressed in angular degrees, for example, how would you express it?

>>96
With π=1, [1] would cease to be the multiplicative identity.
Also, [1] would not be an integer, because 'integer' refers to a specific idea in another number system.

>>97
uh, 180 of course

>>98

>>I honestly did.'t mean π = 1 specifically,

A 1/2 circle(180 degrees)=You're wrong.

>>97
Think about it this way.
It π is greater than a number A such that
Ak=k+k+k
and less than a number B such that
Bk=k+Ak
Those numbers are called "3" and "4".
Moreover, let there be a number, call it D.
Then for any real x, (4D+4D+D+D)x=x i. e. 4D+4D+D+D is the multiplicative identity.
And a number C such that 4D+4D+D+D=C.
Then π must be between 3+C+D+D+D+D and 3+C+D+D+D+D+D

It is actually very arbitrary choosing D such that ten of them add up to the multiplicative identity. Indeed, I could have chosen any other base, perhaps base-7 if I wanted to. You can call it a "whole number" if you want, but it does not change the fact that that given the additive identity (call it "0"), and the multiplicative identity (call it "1"), and using the sets 1, 1+1, 1+1+1, ..., and the set -1, -1-1, -1-1-1, ..., that π would not be found on either of the lists.

The fact is that the term "whole number" is just that: a term. It is not anything other than that, and has no meaning other than its immediate definition of:
0 is within W
If a is within W, then a+1 is within W
Or the integers can have the definition of
All elements of W is within I
If a is within W, then -1*a is within I.
And for the rationals, R, define it to be all numbers r such that there exists two numbers within I, a and b, such that
ar=b.
π cannot be found in either of the lists.

The great fault in your thinking there is that while geometry does not do much multiplication, rescaling is no problem. "1" radian or degree or "2" radians or degrees have no meaning other than assigning something to a scale. However, the real line is not a scale. The distributive property is the very important property, (a+b)c=ab+ac. This is not used for scales, but it is used for all fields.

"there should be a kind of math that treats π as a single whole number"
There is no math that treats any number as a "single whole number." First, define "single whole number." Then we'll talk.

>>96

Not true at all.

We define integers in terms of sets, rationals in terms of integers and reals in terms of rationals.

Pi is defined (the way I was taught) to be twice the smallest solution to the equation Cos x = 0

Cos x being defined in terms of a power series which follows from real analysis, which depends on how you have defined the real numbers.

Now this first root, however you define the integers, will always be between the third and fourth integer.

You can't just decide pi=1. If you want it to be the multiplicative identity, it's no longer the ratio of the circles circumference to it's diameter.

>>99
You're a dipshit.  1/2 of a circle IS pi rad.  So pi in rad is 180, fuckhead.

>>96 Oh, and by the way, you just got gang raped.

Ah, I concede.  I failed hard, guys.

kk people lets remember that i = -1 square root and pi = 3.14

>>105
π ≈ 3.14

Fixed, and lrn2charmap.

Let's make a number system where imaginary numbers just fit in with irrational numbers and integers.  NO SEGREGATION.

>>107
Not possible. They DON'T BELONG IN AN ORDERED FIELD.

>>108
Oh, I get it.  You don't want blacks to play on the same field.  Fuck you, racist shit.

>>108
If you were killed
Tommorow in a table -related accident
I wouldn't give a rats ass because I would
be sitting on my table.

>>109
Actually, only numbers for which all numbers q such that q^2>0 are allowed on ordered fields. Yes, I agree that numbers for which its square is negative just don't belong on ordered fields.

>>111
Is that a crack at blacks' abilities now?  Oh fuck this.

YOOOOOU

THAT SOULJAH BOY

>>112
lol

>>100
"single whole number": number that is expressible without parts of the unit in the given base

what fuck else you thought he could have meant by that, but no you like to post angrily at others, grrrrrrr

>>115
Use precise words rather than vague ones. What is a "unit in the given base"?

>>1
imaginary numbers are imaginary, pie is a tasty treat that is certainly real.

gajillion is an imaginary number

>>116
right.  base refers to number of digit symbols.  unit refers to that amount we name 1.  You couldn't figure that out from the words given earlier?  maybe you are in a different country?  I know that there are some idiomatic differences in English from place to place.