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0.9999999...=1.0

Name: Hump4us 2007-10-06 22:29

It's a fact. Deal with it, bitches.

Name: Pasis 2007-10-10 15:27

>>39

This is where one gets the meaning of sequences and series wrong. Let's just say I give you 0.888, I bet another form to put it is 0.8+0.08+0.008, no? It is a series where the ratio for each consecutive term is 0.1 and the sum of these three terms is 0.888. If I give you 0.929292, I can place it as 0.92+0.0092+0.000092, where the ratio is 0.01. Add them together, you get 0.929292. It is the same as 0.99999999999999.... where I can keep placing it as 0.9+0.09+0.009+0.0009+0.00009+... and henceforth until the number of terms reaches infinity and the geometric ratio of each consecutive term is 0.1.

e and Pi are both constants. They have a fixed value in which both of their values are not in a definite series. 3.1419... has no definite area where one can put a series into it because there is no definite pattern in the constant itself. It is a number as a whole. But I can place an easily definable value like 0.999 as 0.9+0.09+0.009. It is true when you sum the three terms all together, no? This will be true for 0.99999.... as 0.9+0.09+0.009+...

I guess one has yet to learn about geometric progression, yes?

>>40

I do not think one can put a decimal point 1 at infinite decimal's end. ._.

Seem logical, but it is wrong in my opinion. One cannot define a point in infinity, therefore no number could be placed there. Maybe an unknown, but not a number.

Name: Pasis 2007-10-10 15:33

>>39

On another note, that proof is also true and plausible, I believe.

Try dividing 1 by 3. You'll get an imaginary infinite decimal of 3's, 0.33333.... Same goes with 2/3 as 0.66666...

Add them in fraction form, and one will get 1.

Name: Anonymous 2007-10-10 18:34

>>38
All real numbers are the limits of cauchy sequences of rationals.

Two cauchy sequences with the same limit represent the same number.

Lim (n->inf) [1] = 1
0.999... =(by definition) Lim (n->inf) [1-(1/10)^n] = 1

=>0.999...=1

You can classify the cauchy sequences representing 1 as much as you want, but that doesn't change the fact that 0.999... and 1 are one and the same object.  The LIMIT of these sequences.

Name: Anonymous 2007-10-10 19:27

>>41

e = Sum(n=0->inf)[1/n!]

Name: Anonymous 2007-10-10 19:39

http://en.wikipedia.org/wiki/.999_%3D_1#Skepticism_in_education

Like all things worth discussing, this one already has an impressive article on the 'pedia.

Name: Anonymous 2007-10-10 22:17

>>43
Did you imagine yourself do be refuting something I said, rather than simply restating my point?

Name: Anonymous 2007-10-11 0:40

>>43
brainwashed

Name: Pasis 2007-10-11 0:54

>>44

Whoops. I did not see that it is a sum of a series. My apologies on that. But wait. Yes, it is a sum of a series, but not the sum of a *geometric* series, where the ratio of any two consecutive terms must be constant. Euler's number does not have a definite geometric series. Which is why it generates such a number to begin with.

0.9999... is a geometric series. It has a definite ratio, unlike the two other constants you mentioned(Yes, they are the sum of a series, but they are not geometric in nature).

Try finding a *geometric* series for Pi, if I were to give the number as a whole, there is no definite way one can put it.

Name: Anonymous 2007-10-11 8:10

>>48

That's alright. It sounds like you're foreign, so I don't blame you for not being completely rigorous in putting across what you intended to mean. There isn't a geometric series for pi or e. I'm guessing you don't mean Euler's constant by "Euler's number", but e. Euler's constant we know almost nothing about.

Also, <<One cannot define a point in infinity, therefore no number could be placed there. Maybe an unknown, but not a number.>>

Complex analysis (along with many topological spaces) frequently makes use of a "point at infinity" which helps immeasurably in theoretical proofs and so on. It might not be as intuitive a notion, but it's treated in the same way as other complex numbers.

Name: Pasis 2007-10-11 10:28

>>49

Me, what? Foreign? Naw, I'm from Earth. This is an international board, no? Nobody is foreign. ._.

Err... on your second statement. I'ma flip a dictionary first(I don't know what is 'topological' and I'ma think about what is one saying).

Name: Anonymous 2007-10-11 12:32

This is an international board, no?
Prove it.
Nobody is foreign. ._.
Well, at least sub-Saharan Africans are not welcome here.

Name: Anonymous 2007-10-11 19:59

GODDAMIT WHY IS NO-ONE CARING THAT REDCREAM MADE A FALLACIOUS STATEMENT.

Name: Pasis 2007-10-11 20:34

>>51

Well, I guess if people from all over the world could have access to it... Unless I am wrong - only selected countries get to access 4chan. Don't know, man. I just arrived here.

Eh? 4chan seems like an international board to me...

Name: RedCream 2007-10-11 22:47

>>52
He hee he heee!

Name: Anonymous 2007-10-12 3:36

>>40
You can as soon as you fill in those numbers in the 0...1.

Name: Anonymous 2007-10-12 7:21

>>53
This is not an image board so I can't show it right, but
http://upload.wikimedia.org/wikipedia/commons/b/b1/Apartheid_sign.JPG
This is what I meant :-/

Name: Pasis 2007-10-12 8:45

>>56

o_o...

What now, does that mean I am not allowed here?

Funny, but is this true? /swt

I hope not. Because I am not white.

Name: Anonymous 2007-10-12 9:14

>>57
Well, we do make a few exceptions. What race/nationality are you?

Name: Pasis 2007-10-12 10:01

>>58

Ai. What does one think?

What ethnic background does one think I am from?

I wanna see guesses first, I'm curious. ._.

Name: Anonymous 2007-10-12 11:13

>>59
Sand nigger

Name: Anonymous 2007-10-12 11:23

0.9999999... is slightly less than 1.

Name: Anonymous 2007-10-12 11:24

>>61
Yeah, but so close it doesn't really matter.

Name: Pasis 2007-10-12 11:42

>>60

No. Not exactly.

Try some more. ._.

Name: Anonymous 2007-10-12 11:56

>>63
Indian? South Asian?

Name: Pasis 2007-10-12 12:20

>>64

Not even close. I ain't dark skinned in colour, man.

I'm Asian. To be exact - Chinese, or how you put it... Chink. ._.

Bet you can't guess my nationality.

Name: Anonymous 2007-10-12 12:51

>>65
>>56 here.
Of course you are welcome. :-) Only niggers and other non-humans aren't, but they never come here anyway so rules are as enforced.

Name: Anonymous 2007-10-12 13:30

>>65
Yellows are allowed, so you're fine.

As for your nationality, maybe you're from Hong Kong?

Name: Pasis 2007-10-12 14:16

/swt

And I thought I was already bad enough with the racial slurs adn insults. You guys have a fence up specially for them. o_o

Hail Anonymous.

No, I am not from Hong Kong. Further from Hong Kong. Probably out of the guesses of most people, if not all. /heh

Name: Anonymous 2007-10-12 19:09

>>54

Fuck you and your ignorance of general topological properities

Name: RedCream 2007-10-13 0:39

>>69
Well, it was a minor error, and few people cared anyway ... largely since you're such a gaping asshole of a fagswallower.

Still, 0.999... = 1 and there's nothing you can do about it anyway.  Algebraically you can arrive at that conclusion, and the concept of limits supports it, and that's good enough for me.

Name: Anonymous 2007-10-13 7:35

c = 0.999...
10c = 9.999...

10c - c = 9.999... - 0.999...
9c = 9
c = 1


If you still don't believe 0.999... = 1, don't worry. It's because of your poor education and not because you're stupid.

Name: Anonymous 2007-10-13 9:09

1 - 0.999999 = 1/10^n -> n -> infinite
Thus (1-0.9999)* 10^n = 1
According to you 0 * 10^n = 1 thus 0=1
AMIRITE?

Name: Anonymous 2007-10-13 9:52

0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

is as good as 1.

Name: Anonymous 2007-10-13 10:53

>>73
and then with that logic 0 = 1, as >>72 said.

Name: Anonymous 2007-10-13 12:06

>>70


An error is an error, regardless of how large.

Name: Anonymous 2007-10-13 12:43

>>71
you can't do arithmetic on infinite digits, you'd never finish

Name: RedCream 2007-10-13 14:18

>>72
No, you dingleberry!  As n → ∞, your algebraic operation becomes invalid.

Name: Anonymous 2007-10-13 16:14

>>7

I'm probably not up to your standard of Science, but surely if photons move at the speed of light then it must be possible for other particles to move at that speed also, given that we are all made of the same fundamental strings.

Name: Anonymous 2007-10-13 17:11

>>78
Photons have zero rest mass. Nothing else has rest mass.

Name: Anonymous 2007-10-13 18:04

>>78
String theory ftl.

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