Curse

Rushin Roulette · Jun 08, 2008, 05:13 PM // 17:13

Quote:

Originally Posted by Buzzer

Really? How can you have a 1 after infinite zeroes?

Its one position after the final nine behind the decimal point in 0.999∞

Lasareth · Jun 08, 2008, 05:51 PM // 17:51

http://encyclopediadramatica.com/Divide_by_zero

around · Jun 08, 2008, 08:26 PM // 20:26

GUYS LERN2LIMITS KTHNXBAI.

Tevash Szat has posted the 'best' proof here.

And also-maths has no dealings with common sense or intuition.

Rahja-they differ by the wiedth of a line (ie 0).

awesome sauce · Jun 08, 2008, 11:04 PM // 23:04

Ok, I have thought about this and I think that I have absolute proof that 1-.9999∞ =/=0.

.999∞ = 1-1/∞ , because both represent a value infinitely close to 1.

Because 1/∞ is undefined you need to use lim 1-1/x for a definite value.
.................................................. .......x->∞

Thus 1 - .999∞ = lim 1- (1-1/x), which simplifies to lim 1/x.
.......................x->∞.....................................x->∞

1/x never reaches zero.... if it did its antidervative ln(x) (+c) would have critical points, which is ABSOLUTELY NOT TRUE.

Eh?

Lasareth · Jun 08, 2008, 11:53 PM // 23:53

Quote:

Originally Posted by awesome sauce

.999∞ = lim 1-1/x ,
...........x->∞

equals

Quote:

Thus 1 - .999∞ = lim 1- (1-1/x)
.......................x->∞.....................................x->∞

how?

And unless I'm being whooshed you're trying to debate something that's been established for quite a while through real proofs.

Lord Sojar · Jun 09, 2008, 12:19 AM // 00:19

For the last time, it infinitely approaches 1, but it never reaches it, because the .9 is extended into infinity. You can safely round the number up, but it does not truly equal one.

This is evidenced in quantum mechanics, particularly quark separation. It takes a unit of 1 energy to separate a set of quarks. However, the most energy that can be output is .99999∞. Because that number never reaches 1, the quarks never separate.

Another example is actually in science fiction, but is substantiated by science. In Star Trek, the vessels could travel warp 9.9999∞, but they could never travel warp 10. However, they could go around the theoretical speed of warp 10 using alternative technologies (the Borg used this to achieve "Warp 13" and outpace any federation ship, known as Trans-Warp). The concept behind it was simply that to achieve warp 10 would require a space time rip, folding space in on itself, collapsing into itself. My explanation is sloppy, but essentially the same is true for surpassing the speed of light. The closer you get to the speed of light, the slower time passes. I really don't feel like going into my basement and through my doctrine books to find quantum theory and mechanics books... so just go with it.

Think of 1 as warp 10. You can get infinitely close to it, but you never actually get to it. Sorry, use Riemann theory, not Archimedean theory. I am a doctor of physics, not math.

awesome sauce · Jun 09, 2008, 03:03 AM // 03:03

Ok first of all I need to correct my proof.

.999∞ = 1-1/∞ , not lim 1-1/x (which IS 1)
............................x->∞

So, I've corrected the rest of the proof accordingly.

Quote:

Originally Posted by Lasareth

equals

how?

And unless I'm being whooshed you're trying to debate something that's been established for quite a while through real proofs.

Subtraction limit law, look it up.

Also, I'm not sure what exactly has been "established" but I thought the whole purpose of this thread was to try and come up with a proof contradicting the original statement that 1 - .99999∞ = 0, and I'm pretty sure that's exactly what I did.

Quote:

Originally Posted by Rahja the Thief

For the last time, it infinitely approaches 1, but it never reaches it, because the .9 is extended into infinity. You can safely round the number up, but it does not truly equal one.

It doesn't approach anything, it's a number. That's why i've been using 1-1/x, which DOES have a limit and represents the same value as x goes to infinity.

Lord Sojar · Jun 09, 2008, 04:32 AM // 04:32

Quote:

Originally Posted by awesome sauce

It doesn't approach anything, it's a number. That's why i've been using 1-1/x, which DOES have a limit and represents the same value as x goes to infinity.

Yes, it does approach 1. It gets closer and closer to 1 for each additional 9 added to the irrational number. Infinite numbers of 9 do not round up. This is highly debated in mathematics. Mathematicians agree that .9 repeating does indeed equal 1. Physicists believe it doesn't. I fit into the physicists area. It really depends on what mathematical theorems you utilize.

Keep in mind, mathematics is a hard science, and therefore the concept is typically accepted that .9999 repeating is indeed 1.

However, many parts of physics are soft sciences, and in that instance, the concept of infinity is not fully understood. Infinity in physics stretches beyond the mathematical term. Rather than just meaning never ending, it also adds in parallelism, coupled dimensions, factor theory, and quantum law. Physics based math utilizes chaos to make order, whereas math uses order to make order. Mathematics has defined ends, even though infinity means never ending, there is a point at which it "ends."

Think of it this way:

Mathematics, the width of a line is determined as 0, as it is 1 dimensional in standard mathematics, and that is the difference between .999 repeating and 1.

However, in physics, the line has many dimensions, stretching not only through a singular dimension, but also time, empty space, diffused dimensions, etc. That line can be more than 0. The width of a hypersphere is an excellent example. In physics, a line can also be defined as a 1 dimensional sphere. What about those lines added into 4 dimensions using the volume of a hypersphere?

V4= [(pi^2)(R^4)]
____________
2

Thus, the limit -R------->12 4/3pi (R^2-z^2)^(3/2) dz

as a simplified hypersphere volume limit.

To truly get .999 repeating to equal 1, you would have to add .111 repeating to achieve that. Despite .999 repeating being very close to 1, it never reaches it, just becomes so infinitely small, that eventually time ceases to function and it actually becomes 0. Don't ask... it is the reflexive property of pure equalities, in such that a number equals itself, not a different number. You can use all the proof you want, but you cannot fully grasp multi dimension theory, in which a line has other attributes, and stretches to 0 and infinity at the same point. I know, it sounds odd, but it is true.

I guess an easier way to think of it would be in terms of time.

1 second = 1 second.

.9999 repeating seconds = infinite amount of time looping into the loss of time, thus it is zero in that sense.

That is why 0 doesn't equal zero if you are talking about the true value of zero. Zero is actually all numbers except itself, at least in physics mathematics.

RavagerOfDreams · Jun 09, 2008, 05:28 AM // 05:28

to me it seems like you can't prove the equation wrong but neither can you prove it correct

do i win?

Rhamia Darigaz · Jun 09, 2008, 09:42 AM // 09:42

Quote:

Originally Posted by Tevash Szat

This statement is quite valid. Here is a calculus proof.

You can express 0.9999.... in terms of a sequence with the summation from n=1 to n=infinity of 9(1/10)^n

That is just a simple geometric series that converges. To find the number a geometric series converges to, you use (an1 * r)/(1-r) where an1 = 9 and r = 1/10.

Thus, (9/10)/(1-1/10) => (9/10)/(9/10) = 1

I can just go on with all of the other proofs there are, but most of them are in higher math ie higher than Multivariable Calculus or Differentials and really hard to type here.

i like this proof.
also, magic the gathering

lacasner · Jun 09, 2008, 05:09 PM // 17:09

lim (x-1) = 0.
x -> 1-

There ya go.

around · Jun 09, 2008, 09:00 PM // 21:00

This is maths, not physics. We don't have truck with 'real world' in here.

Kerwyn Nasilan · Jun 09, 2008, 11:15 PM // 23:15

This whole thread makes my head asplode

kev read · Jun 09, 2008, 11:37 PM // 23:37

Quote:

Originally Posted by mrmango

1/3=.333inf
1/3 * 3 = 1
.333inf * 3 =.999inf
1= .999inf

QFT...

I was gonna post this but you beat me to it...

**Marty Silverblade** · Jun 10, 2008, 02:15 AM // 02:15

Ok, second attempt

If;

1/2=0.5, and 0.99/2=0.4999999etc, then 1=/=0.99

Makes sense to me.

Kanyatta · Jun 10, 2008, 02:23 AM // 02:23

Quote:

Originally Posted by Marty Silverblade

1/2=0.5, and 0.99/2=0.4999999etc, then 1=/=0.99

Possibly the counterexample to finally win the thread.

poobert · Jun 10, 2008, 11:50 AM // 11:50

Quote:

Originally Posted by Marty Silverblade

Ok, second attempt

If;

1/2=0.5, and 0.99/2=0.4999999etc, then 1=/=0.99

Makes sense to me.

0.49999999999... = 0.5 actually

Divinitys Creature · Jun 10, 2008, 12:23 PM // 12:23

Never knew you were a Physicist Rahja.

Anyway I agree with you. (except for your typo 0.1111 when you mean 0.0000...0001)

Now 1 - 0.999999∞ = 10^-∞

Attempted proofs are then saying that 10^-∞ = 0 WTF! It's obviously not consistent with the rest of mathematics because 10^-∞ is the infinitessimal and in mathematics this is greater than zero or calculus wouldn't work.

From another point of view, information is destroyed in the process of equating 0.99999∞ to 1 and information has to be conserved. I can't even remember the last time I read any proof about the conservation of information TBH though.

poobert · Jun 10, 2008, 12:53 PM // 12:53

Quote:

Originally Posted by Divinitys Creature

Attempted proofs are then saying that 10^-∞ = 0 WTF! It's obviously not consistent with the rest of mathematics because 10^-∞ is the infinitessimal and in mathematics this is greater than zero or calculus wouldn't work.

Well then it is funny how mathematicians have made the property an axiom in field theory.

What you meant to say, is that calculus wouldn't work if the opposite is true. Something that extends in to infinity but converges towards a limit has to have a finite value otherwise you couldn't integrate anything.

The integral of a wavefunction would always be smaller than 1!!! Have you done any quantum mechanics?? the implications would be psycho to say the least.

Snow Bunny · Jun 10, 2008, 07:17 PM // 19:17

Quote:

Originally Posted by poobert

0.49999999999... = 0.5 actually

Only if you're rounding, which was established at the beginning to not be legitimate.
I'm pretty sure Marty's right here. I haven't done maths for 3 years, but I'm pretty sure his logic there wins.